Datasets:
christopher
/
oeis

Dataset card Data Studio Files
xet
Community
2
sequence_id
stringlengths
7
7
sequence_name
stringlengths
4
573
sequence
sequencelengths
1
348
keywords
sequencelengths
1
8
score
int64
1
2.31k
offset_a
int64
-14,827
666,262,453B
offset_b
int64
0
635M
⌀
cross_references
sequencelengths
1
128
⌀
former_ids
sequencelengths
1
3
⌀
author
stringlengths
7
231
⌀
timestamp
timestamp[us]date
1999-12-11 03:00:00
2025-04-28 00:58:08
filename
stringlengths
29
29
hash
stringlengths
32
32
A358701
a(n) is the least number > 1 that needs n toggles in the trailing bits of its binary representation to become a square.
[ "4", "5", "7", "14", "79", "831", "6495", "247614", "7361278", "743300286", "121387475838" ]
[ "nonn", "base", "hard", "more" ]
34
0
1
[ "A000120", "A000290", "A001737", "A159918", "A358701" ]
null
Hugo Pfoertner, Dec 16 2022
2024-04-15T16:20:09
oeisdata/seq/A358/A358701.seq
1628cc17a67ce7ea70606a3bbf0614bc
A358702
a(n) is the least k > 0 such that the sum of the decimal digits of k^2 is n, or 0 if no such k exists.
[ "1", "0", "0", "2", "0", "0", "4", "0", "3", "8", "0", "0", "7", "0", "0", "13", "0", "24", "17", "0", "0", "43", "0", "0", "67", "0", "63", "134", "0", "0", "83", "0", "0", "167", "0", "264", "314", "0", "0", "313", "0", "0", "707", "0", "1374", "836", "0", "0", "1667", "0", "0", "2236", "0", "3114", "4472", "0", "0", "6833", "0", "0", "8167", "0", "8937", "16667", "0", "0", "21886", "0", "0", "29614" ]
[ "nonn", "base" ]
5
1
4
[ "A056991", "A067179", "A231897", "A358702" ]
null
Hugo Pfoertner, Dec 04 2022
2022-12-04T08:34:12
oeisdata/seq/A358/A358702.seq
0fa7cd385a352b46e3bd761c31b90abf
A358703
Sliding numbers: totals, without repetitions, of sums r + s, r >= s, such that 1/r + 1/s = (r + s)/10^k for some k >= 0.
[ "2", "7", "11", "20", "25", "29", "52", "65", "70", "101", "110", "133", "200", "205", "250", "254", "290", "425", "502", "520", "641", "650", "700", "785", "925", "1001", "1010", "1100", "1258", "1330", "2000", "2005", "2050", "2225", "2500", "2504", "2540", "2900", "3157", "3445", "4025", "4250", "5002", "5020", "5200", "6266", "6325", "6410", "6500", "7000" ]
[ "nonn", "base" ]
9
1
1
[ "A103182", "A358703" ]
null
Hugo Pfoertner, Nov 28 2022
2022-11-29T10:15:41
oeisdata/seq/A358/A358703.seq
c2d5288405decf1bab7dbe0eccb92652
A358704
Numbers m such that the sum of the prime divisors and the sum of the nonprime divisors of m^2+1 are both prime.
[ "3", "9", "172", "309", "327", "392", "473", "483", "557", "578", "633", "657", "693", "699", "747", "767", "819", "820", "829", "909", "911", "1007", "1013", "1028", "1030", "1057", "1084", "1141", "1157", "1186", "1252", "1308", "1311", "1382", "1577", "1585", "1620", "1682", "1721", "1722", "1727", "1749", "1841", "1849", "1874", "1972", "2019", "2134" ]
[ "nonn" ]
9
1
1
[ "A193462", "A194039", "A194594", "A358704" ]
null
Michel Lagneau, Nov 27 2022
2022-12-19T09:45:53
oeisdata/seq/A358/A358704.seq
7fe4fe4310b2a7ecb900fae886ba0e08
A358705
Zeroless pandigital numbers whose square has each digit 1 to 9 twice.
[ "345918672", "351987624", "359841267", "394675182", "429715863", "439516278", "487256193", "527394816", "527498163", "528714396", "572493816", "592681437", "729564183", "746318529", "749258163", "754932681", "759142683", "759823641", "762491835", "783942561", "784196235", "845691372", "891357624", "914863275", "915786423", "923165487", "928163754", "976825431" ]
[ "nonn", "base", "fini", "full" ]
24
1
1
[ "A050289", "A199630", "A358705" ]
null
Zhining Yang, Nov 27 2022
2022-12-01T17:21:03
oeisdata/seq/A358/A358705.seq
f8e653619f7ed66a1fb5afc820ed535b
A358706
Erroneous version of A001676.
[ "1", "1", "1", "1", "1", "1", "28", "2", "8", "6", "992", "1", "3", "2", "16256", "2", "16", "16", "523264", "24", "8", "4", "69524373504", "2", "4", "12", "67100672", "2", "3", "3", "7767211311104", "8", "32", "32", "3014494287036416", "6", "24", "120", "2303837503821447168", "192", "32", "96", "341653284209033216", "8", "11520", "48", "798366828940770681028608", "32", "12", "24", "11852230872517975212032", "24", "32", "8", "91678339751618435453288448", "2", "16", "4", "1986677733776616536315084668928", "4", "1", "24", "142211872163171481167115958878208" ]
[ "dead" ]
8
1
7
null
null
null
2022-11-30T07:51:33
oeisdata/seq/A358/A358706.seq
e773307f96ce14aeece227283d17fdb7
A358707
Number of cycles in the grid graph P_10 X P_n.
[ "45", "9779", "2577870", "439673502", "64300829449", "9203308475041", "1322310119854705", "190273063549680295", "27359264067916806101", "3931128009418993765997", "564680431992866012642342", "81106350080343571152166324", "11649258590678717543578165244", "1673159830616398545304368383554" ]
[ "nonn" ]
21
2
1
[ "A140517", "A231829", "A358707" ]
null
Seiichi Manyama, Nov 30 2022
2025-02-16T08:34:04
oeisdata/seq/A358/A358707.seq
1bfb64e7b97ff4a0b0602398dc081881
A358708
Starting from 1, successively take the smallest "Choix de Bruxelles" (A323286) which is not already in the sequence.
[ "1", "2", "4", "8", "16", "13", "23", "26", "46", "43", "83", "86", "166", "133", "136", "68", "34", "17", "27", "47", "87", "167", "137", "174", "172", "171", "271", "272", "236", "118", "19", "29", "49", "89", "169", "139", "178", "278", "239", "269", "469", "439", "478", "474", "237", "267", "467", "437", "837", "867", "1667", "1337", "1367", "687", "347", "177", "277", "477", "877", "1677", "1377", "1747", "1727", "1717", "1734", "1732", "866", "433", "233", "263", "163", "323", "313", "316", "38", "76", "73", "143", "123", "63", "33", "36", "18", "9" ]
[ "nonn", "easy", "base", "fini", "full" ]
87
0
2
[ "A307635", "A323286", "A323454", "A323460", "A358708" ]
null
Alon Vinkler, Nov 26 2022
2025-01-09T13:03:13
oeisdata/seq/A358/A358708.seq
cc33d824690685b74f2cb6346f016236
A358709
a(n) is the number of free, tree-like polyiamonds, of size 3*n+1, with 120-degree rotational symmetry formed of a central triangle and identical, non-intersecting snakes leading from each of its sides.
[ "1", "1", "1", "2", "3", "6", "11", "20", "37", "66", "119", "217", "391", "706", "1274", "2289", "4133", "7435", "13384", "24068" ]
[ "nonn", "more" ]
31
0
4
null
null
John Mason, Jan 10 2023
2023-01-14T08:15:03
oeisdata/seq/A358/A358709.seq
628be365975258bc34beacc9e5b9a568
A358710
Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 2, 2, ..., n, n] into k nonempty submultisets, for 1 <= k <= 2n.
[ "1", "1", "1", "1", "4", "3", "1", "1", "13", "26", "19", "6", "1", "1", "40", "183", "259", "163", "55", "10", "1", "1", "121", "1190", "3115", "3373", "1896", "620", "125", "15", "1", "1", "364", "7443", "34891", "62240", "54774", "27610", "8706", "1795", "245", "21", "1", "1", "1093", "45626", "374059", "1072316", "1435175", "1063570", "485850", "146363", "30261", "4361", "434", "28", "1" ]
[ "nonn", "tabf" ]
47
0
5
[ "A008277", "A020555", "A358710", "A358721", "A358722" ]
null
Marko Riedel, Nov 27 2022
2023-01-05T18:44:31
oeisdata/seq/A358/A358710.seq
87e1ef0818f37fc4dfdf77e3cd054a4f
A358711
Autobiographical numbers: let the k-th digit count the k-th nonnegative integer (A001477(k)) (possibly overlapping) occurrences in the term.
[ "1210", "2020", "21200", "3211000", "42101000", "521001000", "6210001000", "53110100002", "62200010001", "541011000021", "6401101000310", "74011001003100", "840110001031000", "9321000001201000", "94201000012110000" ]
[ "nonn", "base", "fini", "full" ]
47
1
1
[ "A001477", "A046043", "A138480", "A358711" ]
null
Marc Morgenegg, Nov 28 2022
2023-01-25T10:00:05
oeisdata/seq/A358/A358711.seq
7cb33eae86560a1eb9656ad0e15a3873
A358712
Number of self-avoiding closed paths on an n X 6 grid which pass through four corners ((0,0), (0,5), (n-1,5), (n-1,0)).
[ "1", "17", "229", "3105", "44930", "674292", "10217420", "154980130", "2350703747", "35658264301", "540957030465", "8206939419403" ]
[ "nonn", "more" ]
8
2
2
[ "A333513", "A358697", "A358712" ]
null
Seiichi Manyama, Nov 28 2022
2022-11-28T09:59:28
oeisdata/seq/A358/A358712.seq
e68d346ae59b85baf037860b5cf6c749
A358713
Number of self-avoiding closed paths on an n X 7 grid which pass through four corners ((0,0), (0,6), (n-1,6), (n-1,0)).
[ "1", "41", "1081", "26515", "674292", "17720400", "471468756", "12570253556", "335101401877", "8932110760401", "238088717357193", "6346541968642151", "169176879483125528", "4509681115981777876", "120212775466066851264", "3204464007623702644476", "85420126381414152110475", "2277010595175522782497635" ]
[ "nonn" ]
14
2
2
[ "A333513", "A358698", "A358713" ]
null
Seiichi Manyama, Nov 28 2022
2022-11-28T10:02:04
oeisdata/seq/A358/A358713.seq
18bca13cefcbb420f21d529dab411ce8
A358714
a(n) = phi(n)^3.
[ "1", "1", "8", "8", "64", "8", "216", "64", "216", "64", "1000", "64", "1728", "216", "512", "512", "4096", "216", "5832", "512", "1728", "1000", "10648", "512", "8000", "1728", "5832", "1728", "21952", "512", "27000", "4096", "8000", "4096", "13824", "1728", "46656", "5832", "13824", "4096", "64000", "1728", "74088", "8000", "13824", "10648", "97336", "4096", "74088" ]
[ "nonn", "easy", "mult" ]
24
1
3
[ "A000010", "A127473", "A335818", "A358714", "A361148" ]
null
Param Mayurkumar Parekh and Paavan Mayurkumar Parekh, Nov 28 2022
2023-03-10T12:19:45
oeisdata/seq/A358/A358714.seq
72eebcee7e2b65e00cd933504a0c79dc
A358715
a(n) is the number of distinct ways to cut an equilateral triangle with edges of size n into equilateral triangles with integer sides.
[ "1", "2", "5", "26", "220", "3622", "105859", "5677789", "553715341", "98404068313", "31850967186980", "18779046566454536", "20167518569123722322", "39451359692134386945019" ]
[ "nonn", "more" ]
21
1
2
[ "A045846", "A097076", "A290820", "A290821", "A299705", "A300001", "A358715", "A358716" ]
null
Craig Knecht and John Mason, Nov 28 2022
2022-12-06T10:00:30
oeisdata/seq/A358/A358715.seq
d0bbace0767105f75fffddbc6cd160c0
A358716
a(n) is the number of inequivalent ways to cut an equilateral triangle with edges of size n into equilateral triangles with integer sides.
[ "1", "2", "3", "12", "50", "711", "18031", "952013", "92323440" ]
[ "nonn", "more" ]
11
1
2
[ "A224239", "A299705", "A358715", "A358716" ]
null
Craig Knecht and John Mason, Nov 28 2022
2022-12-06T10:00:41
oeisdata/seq/A358/A358716.seq
0d088bccfe540b64408e93300f202913
A358717
A sequence of sorted primes 2 = p_1 < p_2 < ... < p_m such that (p_i + 1)/2 divides the product p_1*p_2*...*p_(i-1) of the earlier primes and each prime factor of (p_i-1)/2 is a prime factor of the product.
[ "2", "3", "5", "11", "19", "37", "73", "109", "1459", "2179", "2917", "4357", "8713" ]
[ "nonn", "full", "fini" ]
18
1
1
[ "A001259", "A358717", "A358718", "A358719" ]
null
Lorenzo Sillari, Nov 28 2022
2024-02-19T22:52:54
oeisdata/seq/A358/A358717.seq
4697ed1e0b17797793a80bb357e4a7ee
A358718
A sequence of sorted primes p_1 = 2, p_2 = 3, p_3 = 5, p_4 =7, p_5 < ... < p_m such that, for i >= 5, (p_i + 1)/2 divides the product p_1*p_2*...*p_(i-1) of the earlier primes and each prime factor of (p_i-1)/2 is a prime factor of the product p_1*p_2*...*p_(i-1).
[ "2", "3", "5", "7", "11", "13", "19", "29", "37", "41", "43", "59", "73", "83", "109", "113", "131", "163", "173", "181", "227", "257", "331", "347", "353", "379", "419", "491", "523", "571", "601", "653", "661", "677", "739", "757", "769", "811", "859", "1091", "1201", "1217", "1297", "1307", "1321", "1459", "1481", "1621", "1721", "2029", "2081", "2089", "2179" ]
[ "nonn" ]
19
1
1
[ "A001259", "A358717", "A358718", "A358719" ]
null
Lorenzo Sillari, Nov 28 2022
2024-02-20T15:30:49
oeisdata/seq/A358/A358718.seq
b3f425bab70154b3b5ced44dca09547c
A358719
A sequence of primes starting with p_1 = 2, p_2 = 3, p_3 = 5, p_4 = 11, p_5 = 13, p_6 = 23, such that, for i >= 7, (p_i + 1)/2 divides the product p_1*p_2*...*p_(i-1) of the earlier primes and each prime factor of (p_i-1)/2 is a prime factor of the product p_1*p_2*...*p_(i-1).
[ "2", "3", "5", "11", "13", "23", "19", "37", "73", "109", "131", "229", "457", "571", "1459", "1481", "2179", "2621", "2917", "2963", "4357", "8713", "49921", "1318901", "3391489", "6782977", "13565953" ]
[ "nonn", "fini", "full" ]
18
1
1
[ "A001259", "A358717", "A358718", "A358719" ]
null
Lorenzo Sillari, Nov 28 2022
2024-02-20T00:45:11
oeisdata/seq/A358/A358719.seq
db427549f6b646480101191117b8fc68
A358720
The lowest positive-integer center for a square spiral whose center lies in an n X n square of nonprimes.
[ "1", "8", "21", "133", "278", "507", "4442", "5383", "22457", "35628", "177291", "194162", "642257", "1062108", "3351690" ]
[ "nonn", "more" ]
11
1
2
[ "A030296", "A357376", "A358720" ]
null
Samuel Harkness, Nov 28 2022
2023-01-01T09:32:16
oeisdata/seq/A358/A358720.seq
71563f2f90c3e65e8353952ef6336770
A358721
Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 1, 2, 2, 2, ..., n, n, n] into k nonempty submultisets, for 1 <= k <= 3n.
[ "1", "1", "1", "1", "1", "7", "11", "8", "3", "1", "1", "31", "139", "219", "175", "86", "28", "6", "1", "1", "127", "1547", "5321", "8004", "6687", "3579", "1329", "359", "71", "10", "1", "1", "511", "16171", "118605", "333887", "472784", "398771", "223700", "89640", "26853", "6171", "1100", "150", "15", "1", "1", "2047", "164651", "2511653", "13045458", "31207637", "41429946", "34621129", "19882236", "8342411", "2668319", "669446", "134075", "21591", "2785", "281", "21", "1" ]
[ "nonn", "tabf" ]
19
0
6
[ "A008277", "A322487", "A358710", "A358721", "A358722" ]
null
Marko Riedel, Nov 28 2022
2022-12-05T06:26:15
oeisdata/seq/A358/A358721.seq
947ab7491d715b53a045164992c2f912
A358722
Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 1, 1, 2, 2, 2, 2, ..., n, n, n, n] into k nonempty submultisets, for 1 <= k <= 4n.
[ "1", "1", "2", "1", "1", "1", "12", "29", "32", "21", "10", "3", "1", "1", "62", "513", "1399", "1857", "1513", "855", "364", "119", "31", "6", "1", "1", "312", "8165", "55704", "155989", "231642", "215250", "139789", "68154", "26135", "8105", "2071", "435", "75", "10", "1", "1", "1562", "125121", "2076531", "12235869", "34100001", "53914814", "54898626", "39436580", "21332108", "9098469", "3160761", "914625", "223740", "46628", "8291", "1245", "155", "15", "1" ]
[ "nonn", "tabf" ]
17
0
3
[ "A008277", "A358710", "A358721", "A358722", "A358781" ]
null
Marko Riedel, Nov 28 2022
2022-12-05T06:26:21
oeisdata/seq/A358/A358722.seq
0c374ad55e5444d54fa507d53792169a
A358723
Number of n-node rooted trees of edge-height equal to their number of leaves.
[ "0", "1", "0", "2", "1", "6", "7", "26", "43", "135", "276", "755", "1769", "4648", "11406", "29762", "75284", "195566", "503165", "1310705", "3402317", "8892807", "23231037", "60906456", "159786040", "420144405", "1105673058", "2914252306", "7688019511", "20304253421", "53667498236", "141976081288", "375858854594", "995728192169" ]
[ "nonn" ]
10
1
4
[ "A000081", "A000108", "A001263", "A011782", "A034781", "A055277", "A065097", "A080936", "A090181", "A109082", "A109129", "A185650", "A209638", "A342507", "A358552", "A358575", "A358577", "A358578", "A358587", "A358589", "A358590", "A358591", "A358723", "A358728" ]
null
Gus Wiseman, Nov 29 2022
2023-01-01T14:46:05
oeisdata/seq/A358/A358723.seq
e86bdc8f27456cb6addde0ca6877ab22
A358724
Difference between the number of internal (non-leaf) nodes and the edge-height of the rooted tree with Matula-Goebel number n.
[ "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "1", "0", "2", "0", "2", "0", "0", "1", "0", "0", "1", "0", "1", "1", "0", "0", "1", "0", "0", "1", "0", "0", "2", "1", "1", "0", "1", "2", "1", "0", "0", "2", "2", "0", "1", "0", "0", "1", "1", "0", "2", "0", "2", "1", "0", "0", "2", "1", "0", "1", "1", "0", "3", "0", "1", "1", "0", "0", "3", "0", "1", "1", "2", "0", "1" ]
[ "nonn" ]
5
1
25
[ "A000040", "A000081", "A000108", "A000720", "A001222", "A001263", "A007097", "A034781", "A055277", "A056239", "A061775", "A080936", "A109082", "A109129", "A112798", "A185650", "A196050", "A206487", "A209638", "A316321", "A342507", "A358552", "A358576", "A358577", "A358578", "A358580", "A358587", "A358592", "A358724", "A358725", "A358726", "A358729", "A358730" ]
null
Gus Wiseman, Nov 29 2022
2022-12-01T08:55:36
oeisdata/seq/A358/A358724.seq
ea5439074bf04eda777ae27bb0ebbd2c
A358725
Matula-Goebel numbers of rooted trees with a greater number of internal (non-leaf) vertices than edge-height.
[ "9", "15", "18", "21", "23", "25", "27", "30", "33", "35", "36", "39", "42", "45", "46", "47", "49", "50", "51", "54", "55", "57", "60", "61", "63", "65", "66", "69", "70", "72", "73", "75", "77", "78", "81", "83", "84", "85", "87", "90", "91", "92", "93", "94", "95", "97", "98", "99", "100", "102", "103", "105", "108", "110", "111", "113", "114", "115", "117", "119", "120", "121" ]
[ "nonn" ]
7
1
1
[ "A000040", "A000081", "A000108", "A000720", "A001222", "A001263", "A007097", "A034781", "A055277", "A056239", "A061775", "A080936", "A109082", "A109129", "A112798", "A185650", "A196050", "A206487", "A209638", "A316321", "A342507", "A358552", "A358576", "A358577", "A358578", "A358580", "A358581", "A358586", "A358587", "A358592", "A358724", "A358725", "A358726", "A358729", "A358730" ]
null
Gus Wiseman, Nov 29 2022
2022-12-01T08:56:02
oeisdata/seq/A358/A358725.seq
cd4fcf098a332ea2517483772def59ff
A358726
Difference between the node-height and the number of leaves in the rooted tree with Matula-Goebel number n.
[ "0", "1", "2", "0", "3", "1", "1", "-1", "1", "2", "4", "0", "2", "0", "2", "-2", "2", "0", "0", "1", "0", "3", "2", "-1", "2", "1", "0", "-1", "3", "1", "5", "-3", "3", "1", "1", "-1", "1", "-1", "1", "0", "3", "-1", "1", "2", "1", "1", "3", "-2", "-1", "1", "1", "0", "-1", "-1", "3", "-2", "-1", "2", "3", "0", "1", "4", "-1", "-4", "1", "2", "1", "0", "1", "0", "2", "-2", "1", "0", "1", "-2", "2", "0", "4", "-1" ]
[ "sign" ]
5
1
3
[ "A000040", "A000079", "A000081", "A000108", "A000720", "A001222", "A001263", "A007097", "A034781", "A055277", "A056239", "A061775", "A080936", "A109082", "A109129", "A112798", "A185650", "A196050", "A206487", "A209638", "A342507", "A358552", "A358576", "A358577", "A358578", "A358580", "A358587", "A358724", "A358726", "A358729", "A358730" ]
null
Gus Wiseman, Nov 29 2022
2022-12-01T08:55:56
oeisdata/seq/A358/A358726.seq
dd38132f3664175973a9662141002a41
A358727
Matula-Goebel numbers of rooted trees with greater number of leaves (width) than node-height.
[ "8", "16", "24", "28", "32", "36", "38", "42", "48", "49", "53", "54", "56", "57", "63", "64", "72", "76", "80", "81", "84", "96", "98", "104", "106", "108", "112", "114", "120", "126", "128", "131", "133", "136", "140", "144", "147", "148", "152", "156", "159", "160", "162", "168", "171", "172", "178", "180", "182", "184", "189", "190", "192", "196", "200", "204", "208" ]
[ "nonn" ]
5
1
1
[ "A000040", "A000081", "A000108", "A000720", "A001222", "A001263", "A007097", "A034781", "A055277", "A056239", "A061775", "A080936", "A109082", "A109129", "A112798", "A185650", "A196050", "A206487", "A209638", "A342507", "A358552", "A358576", "A358577", "A358578", "A358580", "A358587", "A358724", "A358726", "A358727", "A358728", "A358729", "A358730" ]
null
Gus Wiseman, Dec 01 2022
2022-12-02T07:06:09
oeisdata/seq/A358/A358727.seq
1c48a4ef2d53f06f7468b666b4131eea
A358728
Number of n-node rooted trees whose node-height is less than their number of leaves.
[ "0", "0", "0", "1", "1", "5", "10", "30", "76", "219", "582", "1662", "4614", "13080", "36903", "105098", "298689", "852734", "2434660", "6964349", "19931147", "57100177", "163647811", "469290004", "1346225668", "3863239150", "11089085961", "31838349956", "91430943515", "262615909503", "754439588007", "2167711283560" ]
[ "nonn" ]
8
1
6
[ "A000081", "A000108", "A001263", "A034781", "A055277", "A080936", "A109082", "A109129", "A185650", "A358552", "A358577", "A358581", "A358582", "A358585", "A358586", "A358587", "A358589", "A358591", "A358727", "A358728" ]
null
Gus Wiseman, Nov 29 2022
2023-01-01T14:45:41
oeisdata/seq/A358/A358728.seq
528f95c371333913e95ae19405218742
A358729
Difference between the number of nodes and the node-height of the rooted tree with Matula-Goebel number n.
[ "0", "0", "0", "1", "0", "1", "1", "2", "2", "1", "0", "2", "1", "2", "2", "3", "1", "3", "2", "2", "3", "1", "2", "3", "3", "2", "4", "3", "1", "3", "0", "4", "2", "2", "3", "4", "2", "3", "3", "3", "1", "4", "2", "2", "4", "3", "2", "4", "4", "4", "3", "3", "3", "5", "3", "4", "4", "2", "1", "4", "3", "1", "5", "5", "4", "3", "2", "3", "4", "4", "2", "5", "3", "3", "5", "4", "3", "4", "1", "4", "6", "2", "2", "5", "4", "3", "3", "3", "3", "5", "4", "4", "2", "3", "4", "5", "3", "5", "4", "5", "2", "4", "4", "4", "5", "4", "3", "6" ]
[ "nonn" ]
16
1
8
[ "A000040", "A000081", "A000108", "A000720", "A001222", "A001263", "A007097", "A034781", "A055277", "A056239", "A061775", "A080936", "A109082", "A109129", "A112798", "A196050", "A206487", "A209638", "A316321", "A342507", "A358552", "A358576", "A358577", "A358580", "A358592", "A358724", "A358725", "A358726", "A358729", "A358730", "A358731", "A366386" ]
null
Gus Wiseman, Nov 29 2022
2023-10-23T15:17:34
oeisdata/seq/A358/A358729.seq
c219caf58d50508993865f6a1d26c84a
A358730
Positions of first appearances in A358729 (number of nodes minus node-height).
[ "1", "4", "8", "16", "27", "54", "81", "162", "243", "486", "729", "1458", "2187", "4374", "6561", "13122", "19683", "39366", "59049" ]
[ "nonn", "more" ]
6
1
2
[ "A000040", "A000081", "A000108", "A000720", "A001222", "A007097", "A034781", "A055277", "A056239", "A061775", "A080936", "A109082", "A109129", "A112798", "A196050", "A206487", "A209638", "A316321", "A342507", "A358552", "A358576", "A358577", "A358580", "A358592", "A358724", "A358725", "A358726", "A358729", "A358730", "A358731" ]
null
Gus Wiseman, Dec 01 2022
2022-12-02T07:06:02
oeisdata/seq/A358/A358730.seq
7cb3d395efe86dda599cffcfc057173e
A358731
Matula-Goebel numbers of rooted trees whose number of nodes is one more than their node-height.
[ "4", "6", "7", "10", "13", "17", "22", "29", "41", "59", "62", "79", "109", "179", "254", "277", "293", "401", "599", "1063", "1418", "1609", "1787", "1913", "2749", "4397", "8527", "10762", "11827", "13613", "15299", "16519", "24859", "42043", "87803" ]
[ "nonn", "more" ]
6
1
1
[ "A000040", "A000081", "A000108", "A000720", "A001222", "A007097", "A034781", "A055277", "A056239", "A061775", "A109082", "A109129", "A112798", "A196050", "A206487", "A209638", "A289207", "A316321", "A342507", "A358552", "A358576", "A358577", "A358580", "A358592", "A358724", "A358725", "A358726", "A358729", "A358731" ]
null
Gus Wiseman, Dec 01 2022
2022-12-02T07:05:55
oeisdata/seq/A358/A358731.seq
ba415812b539bcd205936e465283f019
A358732
Number of labeled trees covering 2n nodes, half of which are leaves.
[ "0", "12", "720", "109200", "31752000", "15186346560", "10852244282880", "10851787634688000", "14481281691676800000", "24881574582258352358400", "53525038934303849706393600", "140958354488116955062668595200", "446153762528143389466306560000000", "1671353230826683972965623004979200000" ]
[ "nonn" ]
13
1
2
[ "A000055", "A000272", "A001187", "A001349", "A006125", "A006129", "A014068", "A055314", "A163395", "A185650", "A358107", "A358732" ]
null
Gus Wiseman, Dec 01 2022
2024-08-02T11:36:48
oeisdata/seq/A358/A358732.seq
4be3030ce4abd6e34623d944cb6d37b0
A358733
Permutation of the nonnegative integers such that A358654(p(n) - 1) = A200714(n) for n > 0 where p(n) is described in Comments.
[ "0", "1", "2", "3", "4", "5", "7", "6", "8", "9", "11", "10", "12", "13", "17", "14", "18", "15", "16", "19", "20", "21", "22", "27", "23", "28", "29", "24", "25", "26", "30", "31", "32", "33", "34", "43", "35", "44", "36", "37", "45", "46", "47", "38", "39", "40", "41", "42", "49", "48", "50", "51", "52", "53", "54", "55", "56", "69", "57", "70", "71", "58", "59", "60", "72", "73", "74", "75" ]
[ "nonn", "base" ]
51
0
3
[ "A000045", "A048679", "A072649", "A200648", "A200714", "A348366", "A358654", "A358733" ]
null
Mikhail Kurkov, Mar 13 2023 [verification needed]
2024-04-21T22:11:04
oeisdata/seq/A358/A358733.seq
4a960983d5ad553fd8a91c2ac8db8bf3
A358734
Number of down-steps (1,-1) among all n-length nondecreasing Dyck paths with air pockets.
[ "1", "0", "2", "3", "7", "15", "33", "72", "157", "341", "738", "1591", "3417", "7312", "15593", "33145", "70242", "148443", "312893", "657944", "1380437", "2890349", "6040258", "12600623", "26243057", "54572320", "113321233", "235002417", "486735682", "1006950771", "2080889013", "4295799336", "8859716317", "18255789317", "37584488418", "77315114215", "158923017417", "326432444848" ]
[ "nonn", "easy" ]
32
2
3
null
null
Rémi Maréchal, Nov 29 2022
2024-01-18T09:59:22
oeisdata/seq/A358/A358734.seq
e07015b869306d57697feff9c0276cdd
A358735
Triangular array read by rows. T(n, k) is the coefficient of x^k in a(n+3) where a(1) = a(2) = a(3) = 1 and a(m+2) = (m*x + 2)*a(m+1) - a(m) for all m in Z.
[ "1", "1", "1", "1", "4", "2", "1", "10", "16", "6", "1", "20", "70", "76", "24", "1", "35", "224", "496", "428", "120", "1", "56", "588", "2260", "3808", "2808", "720", "1", "84", "1344", "8140", "23008", "32152", "21096", "5040", "1", "120", "2772", "24772", "107328", "245560", "298688", "178848", "40320" ]
[ "nonn", "tabl" ]
37
0
5
[ "A000292", "A040977", "A058797", "A093986", "A204024", "A358735" ]
null
Michael Somos, Mar 15 2023
2023-03-17T10:56:43
oeisdata/seq/A358/A358735.seq
6c6f9bd2efa73a347b2610874ead6cb8
A358736
a(n) is the number of appearances of (9*n + 4) in A358509.
[ "4", "3", "4", "9", "2", "3", "4", "1", "2", "7", "4", "6", "5", "7", "3", "1", "3", "8", "4", "7", "4", "3", "3", "3", "2", "1", "4", "6", "7", "0", "2", "8", "7", "6", "7", "3", "3", "4", "2", "4", "6", "4", "8", "5", "2", "4", "7", "3", "5", "0", "4", "2", "4", "6", "3", "3", "4", "5", "1", "4", "9", "4", "4", "4", "2", "3", "3", "1", "7", "4", "8", "3", "2", "4", "5", "5", "5", "6", "1", "4", "7", "7", "5", "6", "2", "6", "5", "3", "5", "4", "4", "2" ]
[ "nonn" ]
69
0
1
[ "A003462", "A017209", "A358509", "A358736" ]
null
Paul Curtz, Nov 30 2022
2023-03-06T20:34:25
oeisdata/seq/A358/A358736.seq
eabadd8f42ce926631e3a1edc592925d
A358737
a(n) is the greatest prime number dividing A359098(n).
[ "101", "139", "53", "557", "223", "31", "1117", "43", "373", "59", "17", "1123", "281", "5", "563", "23", "47", "1129", "29", "283", "103", "7", "227", "71", "379", "569", "67", "163", "571", "127", "13", "229", "191", "37", "41", "383", "1151", "3", "1153", "577", "11", "17", "89", "193", "61", "43", "83", "1163", "97", "233", "53", "389", "73", "167", "1171", "293" ]
[ "nonn", "base" ]
43
1
1
[ "A006530", "A358737", "A359098" ]
null
Rémy Sigrist, Jan 04 2023
2023-01-04T14:37:16
oeisdata/seq/A358/A358737.seq
d198e0a1dae043ae8286af4dc4995dc3
A358738
Expansion of Sum_{k>=0} k! * ( x/(1 - k*x) )^k.
[ "1", "1", "3", "15", "103", "893", "9341", "114355", "1603155", "25318137", "444689497", "8597568671", "181430298479", "4149361409077", "102229328244837", "2699254206069387", "76038064580742091", "2276259442660623857", "72160287650141753777", "2414950992007231422007" ]
[ "nonn" ]
15
0
3
[ "A001339", "A006153", "A080108", "A358738", "A358740", "A358741" ]
null
Seiichi Manyama, Nov 29 2022
2023-02-18T03:12:49
oeisdata/seq/A358/A358738.seq
e467f688d45f7e8b5d33f6562efa8ad6
A358739
Triangular array read by rows. T(n,k) is the number of n X n matrices A over F_2 such that Sum_{phi} nullity(phi(A)) = k where the sum is over all monic irreducible polynomials in F_2[x] that divide the characteristic polynomial of A, n >= 1, 1 <= k <= n.
[ "2", "6", "10", "84", "210", "218", "5040", "19740", "15330", "25426", "1249920", "5780880", "6939660", "7604610", "11979362", "1259919360", "7533267840", "9297061200", "12276675180", "14280964866", "24071588290", "5120312279040", "34082078607360", "48312946523520", "78970351980240", "88215877158444", "112601184828930", "195647202043778" ]
[ "nonn", "tabl" ]
11
1
1
[ "A002416", "A083402", "A346222", "A358739" ]
null
Geoffrey Critzer, Nov 29 2022
2022-12-15T14:02:24
oeisdata/seq/A358/A358739.seq
dc677c02a99a9dd4749fe15d2d3df12d
A358740
Expansion of Sum_{k>=0} k! * ( k * x/(1 - k*x) )^k.
[ "1", "1", "9", "195", "7699", "482309", "43994741", "5508667927", "906931827831", "189998213001033", "49359340639141993", "15573690455085072011", "5866304418414451865723", "2600416934781350100016717", "1340037064604153376788884701", "794358527033920600533985973631" ]
[ "nonn" ]
11
0
3
[ "A195242", "A358738", "A358740", "A358741" ]
null
Seiichi Manyama, Nov 29 2022
2023-02-18T03:22:52
oeisdata/seq/A358/A358740.seq
42123904aa19a7d8beb49a398bcee956
A358741
Expansion of Sum_{k>=0} k! * ( k * x/(1 - x) )^k.
[ "1", "1", "9", "179", "6655", "400581", "35530421", "4357960999", "706230728379", "146116931998025", "37577989723572001", "11758017370126904091", "4398121660346674034039", "1938019214715102033590029", "993580299268226843514372045", "586357970017371399763899232271" ]
[ "nonn" ]
12
0
3
[ "A355494", "A358738", "A358740", "A358741" ]
null
Seiichi Manyama, Nov 29 2022
2023-02-18T03:26:54
oeisdata/seq/A358/A358741.seq
0511dad935a5c7f5fb633454759448bd
A358742
First of three consecutive primes p,q,r such that p^3 + q^3 - r^3 is prime.
[ "13", "29", "89", "97", "127", "137", "151", "163", "199", "223", "241", "277", "313", "349", "367", "389", "419", "431", "457", "463", "521", "577", "613", "691", "823", "827", "829", "859", "877", "883", "911", "953", "971", "1049", "1087", "1097", "1129", "1151", "1163", "1217", "1409", "1489", "1499", "1579", "1699", "1723", "1867", "1879", "1993", "2089", "2111", "2141", "2293", "2339", "2399", "2411" ]
[ "nonn" ]
18
1
1
[ "A255581", "A358742", "A358743", "A358744" ]
null
J. M. Bergot and Robert Israel, Nov 29 2022
2022-11-29T13:28:47
oeisdata/seq/A358/A358742.seq
907960ea57ea42454147fec23d83dba8
A358743
First of three consecutive primes p,q,r such that p+q-r is prime.
[ "7", "11", "13", "17", "19", "29", "41", "43", "47", "59", "79", "101", "103", "107", "113", "137", "139", "163", "181", "193", "227", "229", "239", "257", "269", "281", "283", "311", "317", "359", "379", "397", "419", "421", "439", "461", "487", "491", "503", "521", "547", "569", "577", "599", "647", "659", "683", "691", "701", "709", "761", "811", "823", "857", "863", "881", "883", "887", "919", "983", "1019" ]
[ "nonn" ]
15
1
1
[ "A136720", "A255581", "A358742", "A358743", "A358744" ]
null
J. M. Bergot and Robert Israel, Nov 29 2022
2022-11-29T13:28:53
oeisdata/seq/A358/A358743.seq
61a41b00d2741043a228e80f13ec34df
A358744
First of three consecutive primes p, q, r such that p + q - r, p^2 + q^2 - r^2 and p^3 + q^3 - r^3 are all prime.
[ "13", "29", "137", "521", "577", "691", "823", "1879", "3469", "4799", "8783", "21569", "25453", "26263", "26591", "27529", "27919", "34607", "39509", "45631", "48869", "53653", "56099", "56633", "57641", "63313", "63809", "67733", "68819", "74381", "76031", "76421", "94781", "97187", "98873", "101279", "105683", "110291", "118967", "119569", "119849", "120577", "123737", "128951" ]
[ "nonn" ]
11
1
1
[ "A255581", "A358742", "A358743", "A358744" ]
null
J. M. Bergot and Robert Israel, Nov 29 2022
2022-12-09T15:43:27
oeisdata/seq/A358/A358744.seq
c9cc15affacec4546d89394b76e3fafb
A358745
a(n) is the least prime p that is the first of three consecutive primes p, q, r such that p^i + q^i - r^i is prime for i from 1 to n but not n+1.
[ "2", "7", "41", "13", "4799", "45631", "332576273", "157108359787", "4001045161" ]
[ "nonn", "more", "hard" ]
17
0
1
[ "A255581", "A358742", "A358743", "A358744", "A358745" ]
null
J. M. Bergot and Robert Israel, Nov 29 2022
2024-03-08T16:04:20
oeisdata/seq/A358/A358745.seq
9b3c5d775722543246f749fd6b20357a
A358746
The number of vertices formed when every pair of n points, placed at the vertices of a regular n-gon, are connected by a circle and where the points lie at the ends of the circle's diameter.
[ "2", "6", "5", "55", "54", "252", "169", "747", "630", "1804", "1381", "3679", "3150", "6690", "5553", "11509", "9846", "18012", "15241", "27237", "24398", "39606", "33577", "56275", "50622", "77058", "69693", "102979", "94770", "135966", "124065", "175593", "162894", "222810", "205885", "279831", "260870", "347178", "321961", "424391", "399042" ]
[ "nonn" ]
33
2
1
[ "A007569", "A146212", "A358746", "A358782", "A358783", "A359009", "A370976", "A370979" ]
null
Scott R. Shannon, Nov 30 2022
2024-03-25T17:41:37
oeisdata/seq/A358/A358746.seq
4c2dd9f08d9d258f948c3a4e9993cfac
A358747
Lexicographically earliest infinite sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = [A007814(n), A007949(n), A324198(n)] when n > 1, with f(1) = 1.
[ "1", "2", "3", "4", "5", "6", "5", "7", "8", "9", "5", "10", "5", "2", "11", "12", "5", "13", "5", "14", "3", "2", "5", "15", "16", "2", "17", "4", "5", "6", "5", "18", "3", "2", "19", "20", "5", "2", "3", "21", "5", "22", "5", "4", "23", "2", "5", "24", "19", "25", "3", "4", "5", "26", "27", "28", "3", "2", "5", "10", "5", "2", "29", "30", "5", "6", "5", "4", "3", "31", "5", "32", "5", "2", "33", "4", "19", "6", "5", "34", "35", "2", "5", "36", "27", "2", "3", "7", "5", "13", "19", "4", "3", "2", "5", "37", "5", "38", "8", "14", "5", "6", "5", "7", "39" ]
[ "nonn", "look" ]
11
1
2
[ "A007814", "A007949", "A305900", "A324198", "A358230", "A358747" ]
null
Antti Karttunen, Dec 01 2022
2022-12-02T13:29:40
oeisdata/seq/A358/A358747.seq
ec3ea37ee4a87e985044f255ffc8ddf4
A358748
Numbers k such that A358669(k) == 1 (mod 4).
[ "6", "18", "22", "26", "30", "34", "38", "50", "58", "66", "74", "90", "98", "102", "106", "122", "126", "130", "138", "142", "146", "158", "170", "174", "178", "182", "186", "194", "198", "210", "222", "226", "234", "238", "258", "262", "270", "274", "278", "286", "290", "298", "314", "322", "330", "338", "346", "350", "362", "370", "374", "378", "382", "386", "394", "398", "406", "410", "426", "442", "466", "482", "486" ]
[ "nonn" ]
5
1
1
[ "A003415", "A016825", "A152822", "A276086", "A358669", "A358748", "A358749", "A358758" ]
null
Antti Karttunen, Dec 06 2022
2022-12-07T14:59:53
oeisdata/seq/A358/A358748.seq
de4fa91629063886452499e91aaa3b07
A358749
Numbers k such that A358669(k) == 3 (mod 4).
[ "2", "10", "14", "42", "46", "54", "62", "70", "78", "82", "86", "94", "110", "114", "118", "134", "150", "154", "162", "166", "190", "202", "206", "214", "218", "230", "242", "246", "250", "254", "266", "282", "294", "302", "306", "310", "318", "326", "334", "342", "354", "358", "366", "390", "402", "414", "418", "422", "430", "434", "438", "446", "450", "454", "458", "462", "470", "474", "478", "490", "506", "510", "518" ]
[ "nonn" ]
4
1
1
[ "A003415", "A016825", "A152822", "A276086", "A358669", "A358748", "A358749", "A358759" ]
null
Antti Karttunen, Dec 06 2022
2022-12-07T14:59:57
oeisdata/seq/A358/A358749.seq
7353f2acc3a746899978f6376f099753
A358750
a(n) = 1 if A349905(n) is a multiple of 4, otherwise 0. Here A349905(n) is the arithmetic derivative applied to the prime shifted n.
[ "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "1", "1", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0" ]
[ "nonn" ]
13
1
null
[ "A001222", "A003415", "A003961", "A010873", "A065043", "A121262", "A246260", "A349905", "A353494", "A358750", "A358752", "A358760" ]
null
Antti Karttunen, Nov 29 2022
2022-12-01T08:56:32
oeisdata/seq/A358/A358750.seq
723fef44d9cbcd406e5b90c63d2d3233
A358751
a(n) = 1 if bigomega(n) == 1 (mod 4), otherwise 0.
[ "0", "1", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "1", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0" ]
[ "nonn" ]
12
1
null
[ "A001222", "A003415", "A003961", "A010051", "A010873", "A066829", "A349905", "A358751", "A358753", "A358761", "A358771" ]
null
Antti Karttunen, Nov 29 2022
2022-12-01T21:08:30
oeisdata/seq/A358/A358751.seq
dac4c1b1fd53fc6dcd61db5b1697e88a
A358752
a(n) = 1 if A349905(n) == 2 (mod 4), otherwise 0. Here A349905(n) is the arithmetic derivative applied to the prime shifted n.
[ "0", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "1", "1", "0", "1", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0" ]
[ "nonn" ]
12
1
null
[ "A001222", "A003415", "A003961", "A010873", "A065043", "A152822", "A246260", "A349905", "A353495", "A358750", "A358752", "A358762" ]
null
Antti Karttunen, Nov 29 2022
2022-12-01T08:56:36
oeisdata/seq/A358/A358752.seq
1bb0f3dc779eb8d9066667ec9a8175a5
A358753
a(n) = 1 if bigomega(n) == 3 (mod 4), otherwise 0.
[ "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "1", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "1", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "1" ]
[ "nonn" ]
12
1
null
[ "A001222", "A003415", "A003961", "A010051", "A010873", "A066829", "A101605", "A349905", "A358751", "A358753", "A358763", "A358773" ]
null
Antti Karttunen, Nov 29 2022
2022-12-01T21:08:34
oeisdata/seq/A358/A358753.seq
a384d1cb7d6af19d25f6e49255ba8e0a
A358754
a(n) = 1 if A053669(n) [the smallest prime not dividing n] is of the form 6m+1, otherwise a(n) = 0.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "nonn" ]
13
1
null
[ "A053669", "A249674", "A353528", "A358754", "A358755", "A358756" ]
null
Antti Karttunen, Dec 03 2022
2024-04-16T02:39:47
oeisdata/seq/A358/A358754.seq
839583f1ecb07bbeda6c0208836b3d02
A358755
a(n) = 1 if A053669(n) [the smallest prime not dividing n] is of the form 6m-1, otherwise a(n) = 0.
[ "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1" ]
[ "nonn" ]
21
1
null
[ "A003987", "A053669", "A276084", "A342051", "A353528", "A353529", "A358754", "A358755", "A358757", "A358842", "A358847" ]
null
Antti Karttunen, Dec 03 2022
2024-04-16T02:39:42
oeisdata/seq/A358/A358755.seq
d8a75b0c09749691f908ec4fcdd11502
A358756
Numbers k such that the smallest prime that does not divide them is of the form 6m+1.
[ "30", "60", "90", "120", "150", "180", "240", "270", "300", "330", "360", "390", "450", "480", "510", "540", "570", "600", "660", "690", "720", "750", "780", "810", "870", "900", "930", "960", "990", "1020", "1080", "1110", "1140", "1170", "1200", "1230", "1290", "1320", "1350", "1380", "1410", "1440", "1500", "1530", "1560", "1590", "1620", "1650", "1710", "1740", "1770", "1800", "1830", "1860", "1920", "1950" ]
[ "nonn" ]
16
1
1
[ "A002476", "A053669", "A353528", "A358754", "A358755", "A358756", "A358757" ]
null
Antti Karttunen, Dec 03 2022
2023-12-05T01:42:06
oeisdata/seq/A358/A358756.seq
fbb638fa50d4bf746ca54e096b9561f6
A358757
Numbers k such that the smallest prime that does not divide them is of the form 6m-1.
[ "6", "12", "18", "24", "36", "42", "48", "54", "66", "72", "78", "84", "96", "102", "108", "114", "126", "132", "138", "144", "156", "162", "168", "174", "186", "192", "198", "204", "210", "216", "222", "228", "234", "246", "252", "258", "264", "276", "282", "288", "294", "306", "312", "318", "324", "336", "342", "348", "354", "366", "372", "378", "384", "396", "402", "408", "414", "420", "426", "432", "438", "444", "456" ]
[ "nonn" ]
16
1
1
[ "A007528", "A053669", "A353530", "A358755", "A358756", "A358757" ]
null
Antti Karttunen, Dec 03 2022
2023-12-05T10:55:46
oeisdata/seq/A358/A358757.seq
65df7098c054231698f42ffed594ce00
A358758
a(n) = 1 if A358669(n) == 1 (mod 4), otherwise 0.
[ "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1" ]
[ "nonn" ]
12
0
null
[ "A152822", "A353488", "A353489", "A358669", "A358748", "A358758", "A358759", "A358771", "A358773" ]
null
Antti Karttunen, Dec 06 2022
2025-03-24T04:12:45
oeisdata/seq/A358/A358758.seq
f0793402cf2291fa0a58dae70b9e5e90
A358759
a(n) = 1 if A358669(n) == 3 (mod 4), otherwise 0.
[ "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0" ]
[ "nonn" ]
13
0
null
[ "A003415", "A152822", "A276086", "A353488", "A353489", "A358669", "A358749", "A358758", "A358759", "A358771", "A358773" ]
null
Antti Karttunen, Dec 06 2022
2025-03-24T05:25:40
oeisdata/seq/A358/A358759.seq
2175a2b30bd67063a20e2702c54d7eec
A358760
Numbers k for which A349905(k) is a multiple of 4, where A349905(k) is the arithmetic derivative applied to the prime shifted k.
[ "1", "6", "15", "16", "21", "22", "26", "36", "40", "46", "51", "55", "56", "57", "62", "65", "74", "77", "81", "87", "90", "91", "94", "96", "100", "115", "118", "123", "126", "129", "132", "136", "140", "142", "152", "155", "156", "159", "161", "166", "178", "183", "185", "187", "194", "196", "201", "209", "214", "216", "217", "218", "219", "221", "225", "232", "235", "237", "240", "247", "250", "256", "259", "262", "276" ]
[ "nonn" ]
16
1
2
[ "A001222", "A003415", "A003961", "A010873", "A028260", "A121262", "A246260", "A327864", "A349905", "A358750", "A358760", "A358761", "A358762", "A358763" ]
null
Antti Karttunen, Nov 29 2022
2023-11-30T02:54:25
oeisdata/seq/A358/A358760.seq
76a82667fc8abc4d7a0b50582476107c
A358761
Numbers k for which bigomega(k) == 1 (mod 4).
[ "2", "3", "5", "7", "11", "13", "17", "19", "23", "29", "31", "32", "37", "41", "43", "47", "48", "53", "59", "61", "67", "71", "72", "73", "79", "80", "83", "89", "97", "101", "103", "107", "108", "109", "112", "113", "120", "127", "131", "137", "139", "149", "151", "157", "162", "163", "167", "168", "173", "176", "179", "180", "181", "191", "193", "197", "199", "200", "208", "211", "223", "227", "229", "233", "239", "241", "243" ]
[ "nonn" ]
11
1
1
[ "A000040", "A001222", "A003415", "A003961", "A010051", "A010873", "A016813", "A026424", "A349905", "A358751", "A358760", "A358761", "A358762", "A358763" ]
null
Antti Karttunen, Nov 29 2022
2022-11-30T16:11:28
oeisdata/seq/A358/A358761.seq
b60333d84b30a31980db5a43410d53ce
A358762
Numbers k for which A349905(k) == 2 (mod 4), where A349905(k) is the arithmetic derivative applied to the prime shifted k.
[ "4", "9", "10", "14", "24", "25", "33", "34", "35", "38", "39", "49", "54", "58", "60", "64", "69", "82", "84", "85", "86", "88", "93", "95", "104", "106", "111", "119", "121", "122", "133", "134", "135", "141", "143", "144", "145", "146", "150", "158", "160", "169", "177", "184", "189", "198", "202", "203", "204", "205", "206", "210", "213", "215", "220", "224", "226", "228", "234", "248", "249", "253", "254", "260", "265" ]
[ "nonn" ]
8
1
1
[ "A001222", "A003415", "A003961", "A010051", "A010873", "A028260", "A246260", "A327862", "A349905", "A358752", "A358760", "A358761", "A358762", "A358763" ]
null
Antti Karttunen, Nov 29 2022
2022-11-30T16:11:32
oeisdata/seq/A358/A358762.seq
bffd9437ba91b561b32a3c43582028da
A358763
Numbers k for which bigomega(k) == 3 (mod 4).
[ "8", "12", "18", "20", "27", "28", "30", "42", "44", "45", "50", "52", "63", "66", "68", "70", "75", "76", "78", "92", "98", "99", "102", "105", "110", "114", "116", "117", "124", "125", "128", "130", "138", "147", "148", "153", "154", "164", "165", "170", "171", "172", "174", "175", "182", "186", "188", "190", "192", "195", "207", "212", "222", "230", "231", "236", "238", "242", "244", "245", "246", "255", "258", "261", "266" ]
[ "nonn", "changed" ]
17
1
1
[ "A001222", "A003415", "A003961", "A004767", "A010051", "A010873", "A014612", "A026424", "A212582", "A226527", "A349905", "A358753", "A358760", "A358761", "A358762", "A358763" ]
null
Antti Karttunen, Nov 29 2022
2025-04-18T18:00:58
oeisdata/seq/A358/A358763.seq
379939da3ee7433cfb5c7362b6b40785
A358764
Largest difference between consecutive divisors of A276086(n), where A276086 is the primorial base exp-function.
[ "0", "1", "2", "3", "6", "9", "4", "5", "10", "15", "30", "45", "20", "25", "50", "75", "150", "225", "100", "125", "250", "375", "750", "1125", "500", "625", "1250", "1875", "3750", "5625", "6", "7", "14", "21", "42", "63", "28", "35", "70", "105", "210", "315", "140", "175", "350", "525", "1050", "1575", "700", "875", "1750", "2625", "5250", "7875", "3500", "4375", "8750", "13125", "26250", "39375", "42", "49", "98", "147" ]
[ "nonn" ]
18
0
3
[ "A002110", "A053669", "A060681", "A276084", "A276086", "A324895", "A353528", "A353529", "A358764" ]
null
Antti Karttunen, Dec 02 2022
2022-12-03T20:26:34
oeisdata/seq/A358/A358764.seq
085ed2d19d130f18f6b1d26adf47b31d
A358765
a(n) = A003415(n)*A276086(n) mod 60, where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.
[ "0", "0", "3", "6", "36", "18", "25", "10", "0", "0", "15", "30", "40", "50", "15", "0", "0", "30", "45", "10", "0", "0", "45", "30", "20", "20", "45", "30", "0", "30", "37", "14", "0", "48", "57", "12", "0", "10", "45", "0", "0", "30", "35", "50", "0", "30", "15", "30", "20", "20", "45", "0", "0", "30", "15", "20", "0", "0", "45", "30", "8", "38", "51", "54", "12", "36", "5", "10", "0", "0", "15", "30", "0", "50", "45", "30", "0", "0", "55", "10", "0", "0", "15" ]
[ "nonn" ]
10
0
3
[ "A003415", "A016825", "A042965", "A067019", "A235992", "A276086", "A358669", "A358765", "A358850" ]
null
Antti Karttunen, Dec 06 2022
2022-12-08T16:32:25
oeisdata/seq/A358/A358765.seq
e923e01760a3f1f98b4e35d69704ed0f
A358766
a(n) = lambda(sigma(n)), where lambda is Liouville's lambda, and sigma is the sum of divisors function.
[ "1", "-1", "1", "-1", "1", "-1", "-1", "1", "-1", "-1", "-1", "-1", "1", "1", "1", "-1", "-1", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "-1", "-1", "-1", "1", "-1", "1", "1", "1", "1", "1", "-1", "1", "-1", "1", "-1", "-1", "-1", "-1", "1", "1", "-1", "-1", "1", "-1", "-1", "-1", "-1", "1", "1", "-1", "1", "1", "1", "-1", "1", "1", "-1", "1", "1", "1", "-1", "-1", "1", "-1", "-1", "1", "1", "-1", "-1", "-1", "1", "1", "1", "1", "-1", "1", "-1", "-1", "1", "1", "-1", "-1", "-1", "1", "-1", "-1", "-1", "-1", "1", "1", "-1", "1", "1", "1", "-1" ]
[ "sign", "mult" ]
15
1
null
[ "A000203", "A001222", "A008836", "A058063", "A358766", "A358767", "A358768", "A359166" ]
null
Antti Karttunen, Dec 18 2022
2022-12-24T03:39:56
oeisdata/seq/A358/A358766.seq
b8154f27c4cca1dabab5262d133dd711
A358767
Numbers k with an even number of prime factors (when counted with multiplicity) in sigma(k), the sum of divisors of k.
[ "1", "3", "5", "8", "13", "14", "15", "18", "22", "23", "24", "27", "28", "34", "36", "37", "38", "39", "40", "42", "44", "49", "50", "53", "58", "59", "61", "62", "63", "65", "66", "68", "69", "70", "73", "76", "77", "81", "82", "83", "84", "86", "89", "90", "94", "99", "100", "102", "103", "104", "110", "111", "112", "114", "115", "116", "119", "120", "121", "124", "125", "131", "132", "133", "134", "135", "139", "140", "142", "144" ]
[ "nonn" ]
6
1
2
[ "A000203", "A001222", "A058063", "A358766", "A358767", "A358768", "A359167", "A359168" ]
null
Antti Karttunen, Dec 19 2022
2022-12-19T15:07:05
oeisdata/seq/A358/A358767.seq
3de3ccc00ec8a62d5c215c7d7cbd869c
A358768
Numbers k with an odd number of prime factors (when counted with multiplicity) in sigma(k), the sum of divisors of k.
[ "2", "4", "6", "7", "9", "10", "11", "12", "16", "17", "19", "20", "21", "25", "26", "29", "30", "31", "32", "33", "35", "41", "43", "45", "46", "47", "48", "51", "52", "54", "55", "56", "57", "60", "64", "67", "71", "72", "74", "75", "78", "79", "80", "85", "87", "88", "91", "92", "93", "95", "96", "97", "98", "101", "105", "106", "107", "108", "109", "113", "117", "118", "122", "123", "126", "127", "128", "129", "130", "136", "137", "138" ]
[ "nonn" ]
4
1
1
[ "A000203", "A001222", "A058063", "A358766", "A358767", "A358768" ]
null
Antti Karttunen, Dec 19 2022
2022-12-19T15:07:13
oeisdata/seq/A358/A358768.seq
4419c03708e266fd4ebd2dc7013e3718
A358769
a(n) = 1 if n is of the form p * m^2, where p is a prime and m is a natural number >= 1, otherwise 0.
[ "0", "1", "1", "0", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "0", "1", "1", "1", "1", "0", "0", "1", "0", "0", "0", "1", "1", "1", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "1", "1", "0", "1", "1", "0", "1", "0", "1", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "1", "1", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "1", "1", "0", "1", "0", "1", "0", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1", "1" ]
[ "nonn" ]
8
1
null
[ "A007913", "A010051", "A229125", "A358769", "A358770" ]
null
Antti Karttunen, Dec 01 2022
2022-12-01T22:30:59
oeisdata/seq/A358/A358769.seq
d4f446e9a3168edbb078d9d41567686b
A358770
a(n) = 1 if n is of the form p * m^2, where p is an odd prime and m is a natural number >= 1, otherwise 0.
[ "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "1", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "0", "0", "0", "1", "1", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "1", "1", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "1", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1", "1" ]
[ "nonn" ]
8
1
null
[ "A000035", "A007913", "A010051", "A035263", "A249370", "A358769", "A358770" ]
null
Antti Karttunen, Dec 01 2022
2022-12-01T22:31:04
oeisdata/seq/A358/A358770.seq
76bf40fd8dd2dab1e7c090c9e02054f4
A358771
a(n) = 1 if the arithmetic derivative of n is of the form 4k+1, otherwise 0.
[ "0", "0", "1", "1", "0", "1", "1", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0" ]
[ "nonn" ]
9
0
null
[ "A003415", "A003961", "A010051", "A010873", "A165560", "A353494", "A353495", "A358751", "A358771", "A358772", "A358773" ]
null
Antti Karttunen, Dec 01 2022
2022-12-01T22:31:08
oeisdata/seq/A358/A358771.seq
d4d8767d422647d5d2c4cb0234521239
A358772
Numbers whose arithmetic derivative is of the form 4k+1, cf. A003415.
[ "2", "3", "5", "6", "7", "11", "13", "14", "17", "18", "19", "22", "23", "29", "31", "37", "38", "41", "42", "43", "46", "47", "50", "53", "54", "59", "61", "62", "66", "67", "71", "73", "79", "83", "86", "89", "94", "97", "98", "101", "103", "107", "109", "113", "114", "118", "126", "127", "130", "131", "134", "137", "138", "139", "142", "149", "150", "151", "154", "157", "158", "162", "163", "166", "167", "170", "173", "179", "181" ]
[ "nonn" ]
6
1
1
[ "A000040", "A003415", "A235991", "A327862", "A327864", "A358771", "A358772", "A358774" ]
null
Antti Karttunen, Dec 01 2022
2022-12-01T21:08:54
oeisdata/seq/A358/A358772.seq
1824b9154ba073568ae814596e4bc91f
A358773
a(n) = 1 if the arithmetic derivative of n is of the form 4k+3, otherwise 0.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1" ]
[ "nonn" ]
9
0
null
[ "A003415", "A003961", "A010873", "A165560", "A353494", "A353495", "A358753", "A358771", "A358773", "A358774" ]
null
Antti Karttunen, Dec 01 2022
2022-12-01T22:31:11
oeisdata/seq/A358/A358773.seq
9f21eeb2ca7d57c37f7cff73e915155d
A358774
Numbers whose arithmetic derivative is of the form 4k+3, cf. A003415.
[ "10", "26", "27", "30", "34", "45", "58", "63", "70", "74", "75", "78", "82", "90", "99", "102", "105", "106", "110", "117", "122", "125", "146", "147", "153", "165", "171", "174", "175", "178", "182", "190", "194", "195", "202", "207", "210", "218", "222", "226", "230", "231", "234", "238", "245", "246", "250", "255", "261", "270", "273", "274", "275", "279", "285", "286", "298", "306", "310", "314", "318", "325", "330", "333" ]
[ "nonn" ]
5
1
1
[ "A003415", "A235991", "A327862", "A327864", "A358772", "A358773", "A358774" ]
null
Antti Karttunen, Dec 01 2022
2022-12-01T21:09:03
oeisdata/seq/A358/A358774.seq
97c33ebf032c9014e183b7a98f90d0c4
A358775
a(n) = 1 if the prime factorization of n has an even number of prime factors that sum to an odd number, otherwise 0.
[ "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0" ]
[ "nonn" ]
7
1
null
[ "A000035", "A007814", "A065043", "A353374", "A356163", "A358775", "A358776" ]
null
Antti Karttunen, Dec 01 2022
2022-12-01T22:31:16
oeisdata/seq/A358/A358775.seq
cc3c51c4c591a068bc9ac8ada87b3d4c
A358776
Positive integers with an even number of prime factors (counting repetitions) that sum to an odd number.
[ "6", "10", "14", "22", "24", "26", "34", "38", "40", "46", "54", "56", "58", "62", "74", "82", "86", "88", "90", "94", "96", "104", "106", "118", "122", "126", "134", "136", "142", "146", "150", "152", "158", "160", "166", "178", "184", "194", "198", "202", "206", "210", "214", "216", "218", "224", "226", "232", "234", "248", "250", "254", "262", "274", "278", "294", "296", "298", "302", "306", "314", "326", "328", "330", "334" ]
[ "nonn" ]
7
1
1
[ "A028260", "A036554", "A249370", "A335657", "A345452", "A358775", "A358776" ]
null
Antti Karttunen, Dec 01 2022
2022-12-01T21:09:12
oeisdata/seq/A358/A358776.seq
99a487d9c4a9643cb8739a08f37beee6
A358777
Dirichlet inverse of A353557, the characteristic function of odd numbers with an even number of prime factors (counted with multiplicity).
[ "1", "0", "0", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "-1", "0", "-1", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "-1", "0", "0", "0", "-1", "0", "-1", "0", "-1", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "-1", "0", "1" ]
[ "sign", "easy" ]
41
1
225
[ "A046315", "A046337", "A065043", "A166698", "A323239", "A353557", "A353558", "A358777", "A358778", "A359589", "A359595", "A359596", "A359598", "A359599", "A359607", "A359608", "A359609", "A359763", "A359773", "A359780", "A359814", "A359815", "A366265" ]
null
Antti Karttunen, Dec 20 2022
2023-11-23T15:13:13
oeisdata/seq/A358/A358777.seq
39f28574b6f77931486b399821e00405
A358778
Positions of positive terms in A358777, which is the Dirichlet inverse of A353557.
[ "1", "135", "189", "225", "297", "315", "351", "375", "441", "459", "495", "513", "525", "585", "621", "693", "735", "765", "783", "819", "825", "837", "855", "875", "975", "999", "1029", "1035", "1071", "1089", "1107", "1155", "1161", "1197", "1225", "1269", "1275", "1287", "1305", "1365", "1375", "1395", "1425", "1431", "1449", "1521", "1593", "1617", "1625", "1647", "1665", "1683", "1715", "1725", "1785" ]
[ "nonn" ]
12
1
2
[ "A046317", "A353557", "A358777", "A358778" ]
null
Antti Karttunen, Dec 23 2022
2022-12-23T16:22:39
oeisdata/seq/A358/A358778.seq
2109d047c36fe947ac4435c0f70c10dd
A358779
a(n) is the maximal absolute value of the determinant of an n X n symmetric matrix using all the integers from 0 to n*(n + 1)/2 - 1.
[ "1", "0", "4", "110", "5911", "652189", "86577891" ]
[ "nonn", "hard", "more" ]
11
0
3
[ "A000217", "A351153", "A351609", "A358779", "A358806", "A358807", "A358808", "A358809" ]
null
Stefano Spezia, Dec 05 2022
2022-12-06T09:57:36
oeisdata/seq/A358/A358779.seq
fcaa4bdd52278ea3c17a3d3835c0eebd
A358780
Dirichlet g.f.: zeta(s) * zeta(2*s) * zeta(3*s) * zeta(4*s).
[ "1", "1", "1", "2", "1", "1", "1", "3", "2", "1", "1", "2", "1", "1", "1", "5", "1", "2", "1", "2", "1", "1", "1", "3", "2", "1", "3", "2", "1", "1", "1", "6", "1", "1", "1", "4", "1", "1", "1", "3", "1", "1", "1", "2", "2", "1", "1", "5", "2", "2", "1", "2", "1", "3", "1", "3", "1", "1", "1", "2", "1", "1", "2", "9", "1", "1", "1", "2", "1", "1", "1", "6", "1", "1", "2", "2", "1", "1", "1", "5", "5", "1", "1", "2", "1", "1", "1", "3" ]
[ "nonn", "mult" ]
28
1
4
[ "A000688", "A001400", "A046951", "A063966", "A322885", "A358780" ]
null
Vaclav Kotesovec, Mar 14 2023
2023-03-14T13:02:45
oeisdata/seq/A358/A358780.seq
63921826ff95ae8bbf5bdb019c87719f
A358781
Number of multiset partitions of [1,1,1,1,2,2,2,2,...,n,n,n,n] into nonempty multisets.
[ "1", "5", "109", "6721", "911838", "231575143", "99003074679", "66106443797808", "65197274052335504", "90954424202936106523", "173398227073956386079670", "439196881673194611574668282", "1443741072199958276777413001395" ]
[ "nonn" ]
13
0
2
[ "A020555", "A219727", "A322487", "A358722", "A358781" ]
null
Marko Riedel, Nov 29 2022
2022-12-05T08:15:00
oeisdata/seq/A358/A358781.seq
ead5159fe718b2b381daecf31a92c8cf
A358782
The number of regions formed when every pair of n points, placed at the vertices of a regular n-gon, are connected by a circle and where the points lie at the ends of the circle's diameter.
[ "1", "7", "12", "66", "85", "281", "264", "802", "821", "1893", "1740", "3810", "3725", "6871", "6448", "11748", "11125", "18317", "17160", "27616", "26797", "40067", "37176", "56826", "54653", "77707", "74788", "103734", "101041", "136835", "131744", "176584", "172109", "223931", "216900", "281090", "273829", "348583", "337480", "425950", "416641" ]
[ "nonn" ]
28
2
2
[ "A007678", "A344857", "A358746", "A358782", "A358783", "A359009", "A370976", "A370979" ]
null
Scott R. Shannon, Nov 30 2022
2024-03-25T17:43:38
oeisdata/seq/A358/A358782.seq
37ce957f224c67fcc4d62f11ecd8363e
A358783
The number of edges formed when every pair of n points, placed at the vertices of a regular n-gon, are connected by a circle and where the points lie at the ends of the circle's diameter.
[ "2", "12", "16", "120", "138", "532", "432", "1548", "1450", "3696", "3120", "7488", "6874", "13560", "12000", "23256", "20970", "36328", "32400", "54852", "51194", "79672", "70752", "113100", "105274", "154764", "144480", "206712", "195810", "272800", "255808", "352176", "335002", "446740", "422784", "560920", "534698", "695760", "659440", "850340", "815682" ]
[ "nonn" ]
19
2
1
[ "A135565", "A344899", "A358746", "A358782", "A358783", "A359009", "A370976", "A370979" ]
null
Scott R. Shannon, Nov 30 2022
2024-03-25T17:45:03
oeisdata/seq/A358/A358783.seq
8cb2c0116a0ca7fa7fbeec7004f3b5bb
A358784
Size of largest semigroup generated by three n X n boolean matrices.
[ "2", "16", "440" ]
[ "nonn", "hard", "more", "bref" ]
5
1
1
[ "A202140", "A217990", "A358784" ]
null
Jeffrey Shallit, Nov 30 2022
2022-11-30T07:17:13
oeisdata/seq/A358/A358784.seq
51f6e7f12f1a02e279f00f7efe209450
A358785
Number of cycles in the grid graph P_11 X P_n.
[ "55", "23637", "12253948", "3779989098", "975566486675", "245355064111139", "61875355046353061", "15609156135669687673", "3931128009418993765997", "988808811046283595068099", "248581947999911644069460438", "62479777983071973470513443588", "15702642238437709110690166048520" ]
[ "nonn" ]
10
2
1
[ "A231829", "A358785" ]
null
Seiichi Manyama, Nov 30 2022
2025-02-16T08:34:04
oeisdata/seq/A358/A358785.seq
36bf393334d6975e1d996a5de027ef0a
A358786
a(1) = 1. For n > 1, a(n) is least novel k != n such that rad(k) = rad(n) and either k | n or n | k, where rad is A007947.
[ "1", "4", "9", "2", "25", "12", "49", "16", "3", "20", "121", "6", "169", "28", "45", "8", "289", "36", "361", "10", "63", "44", "529", "48", "5", "52", "81", "14", "841", "60", "961", "64", "99", "68", "175", "18", "1369", "76", "117", "80", "1681", "84", "1849", "22", "15", "92", "2209", "24", "7", "100", "153", "26", "2809", "108", "275", "112", "171", "116", "3481", "30", "3721" ]
[ "nonn" ]
7
1
2
[ "A007947", "A358786", "A358971" ]
null
Michael De Vlieger, Dec 08 2022
2022-12-11T10:32:17
oeisdata/seq/A358/A358786.seq
332fd955b309386e24e518b7ac21142d
A358787
a(1)=1; let x=gcd(a(n-1),n); for n > 1, a(n) = a(n-1) + n if x=1 or a(n-1)/x=1, otherwise a(n) = a(n-1)/x.
[ "1", "3", "6", "3", "8", "4", "11", "19", "28", "14", "25", "37", "50", "25", "5", "21", "38", "19", "38", "19", "40", "20", "43", "67", "92", "46", "73", "101", "130", "13", "44", "11", "44", "22", "57", "19", "56", "28", "67", "107", "148", "74", "117", "161", "206", "103", "150", "25", "74", "37", "88", "22", "75", "25", "5", "61", "118", "59", "118", "59", "120", "60", "20", "5", "70", "35", "102", "3", "72", "36" ]
[ "nonn" ]
23
1
2
[ "A133058", "A133579", "A133580", "A255051", "A255140", "A262922", "A264767", "A358787" ]
null
Gary Yane, Nov 30 2022
2022-12-17T08:21:51
oeisdata/seq/A358/A358787.seq
bb500e8dde41c843507db7c67d850d78
A358788
Numbers k such that tau(k^2) + 2*sigma(k^2) and 2*tau(k^2) + sigma(k^2) are both prime.
[ "1", "2", "3", "4", "6", "11", "12", "17", "18", "24", "33", "60", "69", "94", "131", "138", "173", "187", "198", "200", "214", "226", "263", "282", "290", "311", "347", "360", "400", "426", "428", "495", "498", "502", "521", "583", "606", "622", "653", "675", "771", "822", "850", "902", "911", "1013", "1020", "1104", "1127", "1177", "1195", "1215", "1243", "1283", "1366", "1377", "1402", "1500", "1714", "1795" ]
[ "nonn" ]
14
1
2
[ "A000005", "A000203", "A358788" ]
null
J. M. Bergot and Robert Israel, Nov 30 2022
2024-08-27T16:39:29
oeisdata/seq/A358/A358788.seq
f5bd5958bbeac7abc2ab3259f2a70578
A358789
Decimal expansion of Sum_{p prime, p>=3} (-1)^((p-1)/2)*log(p)/p, negated.
[ "5", "4", "5", "6", "8", "1", "2", "7", "2", "7", "9", "5", "1", "2", "7", "9", "0", "1", "4", "8", "9", "5", "3", "2", "3", "8", "3", "3", "8", "0", "0", "4", "0", "3", "8", "3", "4", "7", "5", "2", "5", "2", "8", "0", "5", "4", "1", "4", "2", "7", "4", "4", "6", "5", "4", "0", "7", "5", "9", "8", "6", "6", "3", "9", "2", "8", "8", "7", "3", "6", "5", "3", "1", "4", "8", "7", "2", "7", "2", "6", "4", "0", "9", "6", "2", "8", "7", "8", "6", "2", "1", "5", "1", "4", "1", "6", "1", "2", "3", "2", "3", "8", "8", "5", "7", "9", "2", "6", "6", "6", "6", "2", "1", "9", "0" ]
[ "nonn", "cons" ]
79
0
1
[ "A086239", "A091812", "A136271", "A354295", "A358789" ]
null
Artur Jasinski, Jan 03 2023
2023-01-26T05:27:17
oeisdata/seq/A358/A358789.seq
de77dd5b9d08753462e39dc224f4ec84
A358790
a(n) is the least prime p such that (2*n+1)^2 + p^2 is twice a prime.
[ "3", "5", "3", "3", "5", "5", "3", "7", "3", "5", "5", "3", "3", "7", "5", "11", "5", "3", "7", "5", "5", "3", "13", "3", "5", "11", "3", "13", "5", "5", "5", "5", "7", "7", "5", "31", "5", "7", "3", "11", "19", "3", "3", "5", "11", "5", "5", "3", "7", "19", "5", "3", "11", "5", "5", "5", "3", "7", "5", "31", "5", "5", "3", "3", "19", "11", "3", "7", "5", "11", "41", "17", "13", "13", "5", "29", "5", "7", "3", "5", "5", "5", "13", "13", "5", "5", "3", "11", "13", "5", "19" ]
[ "nonn" ]
11
0
1
null
null
J. M. Bergot and Robert Israel, Dec 01 2022
2022-12-11T11:55:58
oeisdata/seq/A358/A358790.seq
cd9ec70fdf1e3450a41dea89a472fab7
A358791
a(n) = n!*Sum_{m=0..floor(n/2)} binomial(n,2*m)^(-1).
[ "1", "1", "4", "8", "52", "156", "1536", "6144", "84096", "420480", "7453440", "44720640", "974972160", "6824805120", "176504832000", "1412038656000", "42224136192000", "380017225728000", "12893605517721600", "128936055177216000", "4892595136708608000" ]
[ "nonn" ]
18
0
3
[ "A003149", "A358791" ]
null
Vladimir Kruchinin, Dec 01 2022
2023-04-15T06:26:57
oeisdata/seq/A358/A358791.seq
67b9a2262d5d50442d75bad6762c2610
A358792
Numbers k such that for some r we have d(1) + ... + d(k - 1) = d(k + 1) + ... + d(k + r), where d(i) = A000005(i).
[ "3", "10", "16", "23", "24", "27", "42", "43", "45", "46", "49", "57", "60", "62", "67", "82", "92", "113", "117", "119", "122", "146", "151", "152", "157", "158", "159", "182", "188", "192", "193", "197", "198", "222", "223", "226", "228", "235", "242", "268", "270", "272", "274", "286", "288", "320", "323", "328", "334", "337", "361", "372", "373", "378", "381", "386" ]
[ "nonn" ]
48
1
1
[ "A000005", "A001109", "A006218", "A358792", "A358797" ]
null
Ctibor O. Zizka, Dec 01 2022
2025-01-05T19:51:42
oeisdata/seq/A358/A358792.seq
8634a63136dbe582183deb68959b2b69
A358793
Lexicographically earliest sequence of positive and unique integers such that 2*Sum_{k = 1..n} a(k) = Sum_{k = 1..n} a(a(k)) for n > 1 and a(1) = 1.
[ "1", "3", "7", "5", "10", "8", "14", "16", "11", "20", "22", "13", "26", "28", "17", "32", "34", "19", "38", "40", "23", "44", "46", "25", "50", "52", "29", "56", "58", "31", "62", "64", "35", "68", "70", "37", "74", "76", "41", "80", "82", "43", "86", "88", "47", "92", "94", "49", "98", "100", "53", "104", "106", "55", "110", "112", "59", "116", "118", "61", "122", "124", "65", "128" ]
[ "nonn", "easy" ]
49
1
2
[ "A002516", "A105753", "A257794", "A358793" ]
null
Thomas Scheuerle, Dec 01 2022
2025-01-23T10:22:59
oeisdata/seq/A358/A358793.seq
6295b9871e4a0a9d5e308ad48ababc47
A358794
Number of Hamiltonian paths in P_7 X P_n.
[ "1", "44", "688", "12010", "109722", "1620034", "13535280", "175905310", "1449655468", "17198428572", "142545533336", "1580868297042", "13246916541978", "139620415865920", "1183338916049852", "11997107474280224", "102719325162193010", "1010824101911587178" ]
[ "nonn" ]
11
1
2
[ "A332307", "A358794" ]
null
Seiichi Manyama, Dec 01 2022
2022-12-01T10:27:35
oeisdata/seq/A358/A358794.seq
ae31cf0eb3086943d0f5eadad862f3d5
A358795
Number of Hamiltonian paths in P_8 X P_n.
[ "1", "58", "1578", "38984", "602804", "12071462", "175905310", "3023313284", "43551685370", "682958971778", "9735477214522", "144397808917246", "2033155413979838", "29105375742858518", "404654754079984324", "5656098437704094140", "77710312229803403554", "1067886114091399967842" ]
[ "nonn" ]
13
1
2
[ "A332307", "A358795" ]
null
Seiichi Manyama, Dec 01 2022
2023-01-27T13:32:16
oeisdata/seq/A358/A358795.seq
e14aeb6faa3893b5f0951769f8b99b51
A358796
Number of Hamiltonian paths in P_9 X P_n.
[ "1", "74", "3190", "122188", "2434670", "82550864", "1449655468", "43551685370", "745416341496", "20458460935162", "350662618941136", "8977863552693182", "155527664975367738", "3769078188330226854", "66168756974349933990", "1534449253192384210354", "27299151102034089996326", "610935315274446987589872" ]
[ "nonn" ]
19
1
2
[ "A332307", "A358796" ]
null
Seiichi Manyama, Dec 01 2022
2023-01-27T15:36:01
oeisdata/seq/A358/A358796.seq
3c074ca607014cac92314541710ae923
A358797
Numbers r such that for some k we have d(1) + ... + d(k - 1) = d(k + 1) + ... + d(k + r), where d(i) = A000005(i).
[ "1", "6", "11", "16", "17", "19", "31", "32", "34", "34", "37", "43", "45", "47", "52", "63", "72", "89", "92", "92", "97", "117", "120", "120", "126", "126", "126", "146", "150", "154", "156", "158", "159", "178", "179", "182", "184", "190", "197", "217", "219", "221", "222", "232", "234", "260", "264", "267", "272", "276", "298", "304", "306", "310", "314", "317", "317" ]
[ "nonn" ]
21
1
2
[ "A000005", "A001109", "A006218", "A358792", "A358797" ]
null
Ctibor O. Zizka, Dec 01 2022
2025-01-05T19:51:42
oeisdata/seq/A358/A358797.seq
b37630cc46daff6145830f1da994b7fa
A358798
a(1) = 2, a(2) = 3; for n > 2, a(n) is the smallest prime that can be appended to the sequence so that the smallest even number >= 4 that cannot be generated as the sum of two (not necessarily distinct) terms from {a(1), ..., a(n-1)} can be generated from {a(1), ..., a(n)}.
[ "2", "3", "5", "7", "11", "13", "17", "19", "23", "31", "29", "37", "41", "47", "43", "61", "53", "67", "59", "73", "71", "83", "89", "79", "97", "101", "103", "109", "107", "113", "127", "131", "139", "137", "149", "151", "163", "157", "179", "167", "173", "181", "193", "191", "211", "197", "199", "227", "233", "223", "229", "239", "251", "241", "277", "257", "271", "263" ]
[ "nonn" ]
31
1
1
null
null
Travis J Weber, Dec 05 2022
2023-02-17T21:55:57
oeisdata/seq/A358/A358798.seq
44e9be703811da931d68574a2d523542
A358799
a(0) = 0, and for any n >= 0, a(n+1) is the number of ways to write a(n) = a(i) XOR ... XOR a(j) with 0 <= i <= j <= n (where XOR denotes the bitwise XOR operator).
[ "0", "1", "2", "1", "3", "4", "2", "5", "4", "5", "6", "8", "2", "11", "2", "13", "6", "14", "10", "9", "9", "12", "14", "16", "2", "24", "6", "29", "5", "23", "3", "27", "12", "23", "9", "26", "17", "13", "26", "19", "15", "32", "4", "46", "2", "51", "1", "45", "6", "48", "6", "49", "7", "41", "9", "47", "10", "49", "17", "37", "21", "38", "23", "36", "24", "49", "30", "48", "24", "52", "22", "45" ]
[ "nonn", "base" ]
12
0
3
[ "A331614", "A332518", "A358799" ]
null
Rémy Sigrist, Dec 06 2022
2022-12-12T12:15:09
oeisdata/seq/A358/A358799.seq
fd589e8c66fe9104b11c0cce7710e425
A358800
Number of (undirected) paths in the grid graph P_4 X P_n.
[ "6", "146", "1618", "14248", "111030", "801756", "5493524", "36213404", "231727206", "1448346368", "8882264970", "53630707124", "319658314238", "1884696886358", "11010327107946", "63818465537674", "367417387464528", "2102996368589366", "11976130801913690", "67900925937645280", "383491738397537356" ]
[ "nonn", "easy" ]
22
1
1
[ "A288518", "A358800" ]
null
Seiichi Manyama, Dec 01 2022
2023-05-01T15:01:13
oeisdata/seq/A358/A358800.seq
db4d75cfbc53e2c9ebf182487a956dc4