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1999-12-11 03:00:00
2025-04-28 00:58:08
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A359401
Nonnegative integers whose sum of positions of 1's in their binary expansion is greater than the sum of positions of 1's in their reversed binary expansion, where positions in a sequence are read starting with 1 from the left.
[ "11", "19", "23", "35", "37", "39", "43", "47", "55", "67", "69", "71", "75", "77", "79", "83", "87", "91", "95", "103", "111", "131", "133", "134", "135", "137", "139", "141", "142", "143", "147", "149", "151", "155", "157", "158", "159", "163", "167", "171", "173", "175", "179", "183", "187", "191", "199", "203", "207", "215", "223", "239", "259", "261", "262", "263" ]
[ "nonn", "base" ]
8
1
1
[ "A000120", "A029931", "A030190", "A030308", "A048793", "A051293", "A053632", "A070939", "A222955", "A230877", "A231204", "A291166", "A304818", "A326669", "A326672", "A326673", "A359043", "A359401", "A359402", "A359495" ]
null
Gus Wiseman, Jan 05 2023
2023-01-07T09:28:17
oeisdata/seq/A359/A359401.seq
b21673ca4c11abb6a0a52dc0d677373e
A359402
Numbers whose binary expansion and reversed binary expansion have the same sum of positions of 1's, where positions in a sequence are read starting with 1 from the left.
[ "0", "1", "3", "5", "7", "9", "15", "17", "21", "27", "31", "33", "45", "51", "63", "65", "70", "73", "78", "85", "93", "99", "107", "119", "127", "129", "150", "153", "165", "189", "195", "219", "231", "255", "257", "266", "273", "282", "294", "297", "310", "313", "325", "334", "341", "350", "355", "365", "371", "381", "387", "397", "403", "413", "427", "443", "455", "471" ]
[ "nonn" ]
12
1
3
[ "A000120", "A029931", "A030190", "A030308", "A048793", "A051293", "A053632", "A070939", "A222955", "A231204", "A291166", "A304818", "A318283", "A326669", "A326672", "A326673", "A358134", "A359042", "A359401", "A359402", "A359495" ]
null
Gus Wiseman, Jan 05 2023
2023-01-08T01:16:26
oeisdata/seq/A359/A359402.seq
208eb6a0ff360b76bb8e639724dc2398
A359403
Primes that are the concatenation of the first m consecutive k-th powers.
[ "149", "11681", "164729", "1102459049", "1262144387420489", "1472236648286964521369622528399544939174411840147874772641", "1755578637259143234191361824800363140073127359051977856583921" ]
[ "nonn", "base" ]
8
1
1
[ "A007908", "A019521", "A019522", "A284377", "A359403" ]
null
Michel Marcus, Dec 30 2022
2022-12-30T06:31:08
oeisdata/seq/A359/A359403.seq
81278e796a4e1c241fae21df7989da7c
A359404
Number of unordered triples of self-avoiding paths with nodes that cover all vertices of a convex n-gon.
[ "0", "0", "15", "315", "4200", "45360", "433440", "3825360", "31944000", "256164480", "1991877888", "15117822720", "112519680000", "824063385600", "5953789181952", "42518284701696", "300588079104000", "2106258635980800", "14642876032942080", "101081482775691264", "693338799538176000", "4728258324725760000", "32074214121878323200" ]
[ "nonn", "easy" ]
23
4
3
[ "A001792", "A332426", "A359404" ]
null
Ivaylo Kortezov, Dec 30 2022
2023-01-29T23:01:19
oeisdata/seq/A359/A359404.seq
014891554440885827ba65f5582916e1
A359405
Number of unordered pairs of self-avoiding paths with nodes that cover all vertices of a convex n-gon; one-node paths are allowed.
[ "3", "15", "70", "330", "1596", "7840", "38592", "188640", "911680", "4350720", "20507136", "95560192", "440724480", "2014003200", "9128476672", "41074384896", "183618256896", "816062464000", "3607813816320", "15874289958912", "69544309424128", "303465643376640", "1319414897049600", "5717462509158400", "24699433622962176", "106397550709309440" ]
[ "nonn", "easy" ]
22
3
1
[ "A001792", "A332426", "A359405" ]
null
Ivaylo Kortezov, Dec 30 2022
2023-01-29T18:12:14
oeisdata/seq/A359/A359405.seq
5169a8fbf6d86949b12153b3d6155519
A359406
Integers k such that the concatenation of k consecutive primes starting at 31 is prime.
[ "1", "2", "3", "23", "43", "141" ]
[ "nonn", "base", "more" ]
58
1
2
[ "A030996", "A069151", "A280894", "A309191", "A359406" ]
null
Mikk Heidemaa, Dec 30 2022
2023-02-14T02:35:43
oeisdata/seq/A359/A359406.seq
df0d26fb601b4696c92d32a5e02db366
A359407
Product_{n>=1} (1 + a(n) * x^n) = 1 + Sum_{n>=1} (n * (n + 1) / 2) * x^n.
[ "1", "3", "3", "7", "-1", "-8", "-3", "48", "1", "-39", "-6", "34", "-25", "-293", "24", "2649", "-35", "-2104", "-239", "3387", "323", "-15322", "-182", "27551", "-2477", "-121985", "3663", "275053", "-360", "-942231", "-26801", "8245538", "40690", "-7506845", "11479", "19149901", "-297030", "-61205072", "442870", "158934665", "284075", "-490800388", "-3338212" ]
[ "sign", "look" ]
14
1
2
[ "A000217", "A147559", "A359407" ]
null
Seiichi Manyama, Dec 30 2022
2022-12-30T10:55:03
oeisdata/seq/A359/A359407.seq
2d23573be2e01a19753142e340c86f54
A359408
Integers d such that the longest possible arithmetic progression (AP) of primes with common difference d has only two elements.
[ "1", "3", "5", "9", "11", "15", "16", "17", "21", "22", "26", "27", "29", "32", "35", "39", "41", "44", "45", "46", "51", "52", "56", "57", "58", "59", "62", "65", "69", "70", "71", "74", "76", "77", "81", "82", "86", "87", "88", "92", "95", "99", "100", "101", "105", "105", "106", "107", "111", "112", "116", "118", "122", "125", "128", "129", "130", "135", "136", "137", "140", "142", "146", "147", "148", "149", "152", "155" ]
[ "nonn" ]
56
1
2
[ "A007921", "A040976", "A123556", "A173919", "A206037", "A206039", "A206041", "A206045", "A342309", "A359408", "A359409", "A359410", "A360146", "A360735" ]
null
Bernard Schott, Dec 30 2022
2023-02-26T17:42:05
oeisdata/seq/A359/A359408.seq
e8b4698554910907903246f1a84b0f3e
A359409
Integers d such that the largest possible arithmetic progression (AP) of primes with common difference d has exactly four elements.
[ "18", "24", "36", "54", "66", "72", "78", "84", "102", "108", "114", "132", "138", "144", "156", "162", "168", "174", "186", "192", "198", "204", "216", "222", "228", "234", "246", "258", "264", "276", "282", "288", "294", "306", "312", "318", "324", "336", "342", "348", "354", "366", "372", "378", "384", "396", "402", "408", "414", "432", "438", "444", "456", "462", "468", "486" ]
[ "nonn" ]
19
1
1
[ "A007921", "A008588", "A123556", "A206037", "A206039", "A206041", "A342309", "A359408", "A359409", "A359410" ]
null
Bernard Schott, Jan 23 2023
2023-01-29T19:37:45
oeisdata/seq/A359/A359409.seq
452c0ccc27e55dec22b7f97c158666df
A359410
Integers d such that the longest possible arithmetic progression (AP) of primes with common difference d has exactly 6 elements.
[ "30", "60", "90", "120", "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" ]
[ "nonn" ]
24
1
1
[ "A007921", "A123556", "A206037", "A206039", "A206041", "A206045", "A249674", "A342309", "A359408", "A359409", "A359410", "A360146" ]
null
Bernard Schott, Jan 29 2023
2023-02-12T05:38:06
oeisdata/seq/A359/A359410.seq
af7f299ccd406180493557bd1e37471d
A359411
a(n) is the number of divisors of n that are both infinitary and exponential.
[ "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1" ]
[ "nonn", "mult" ]
15
1
8
[ "A037445", "A049419", "A077609", "A080948", "A138302", "A246600", "A318672", "A322791", "A325989", "A359081", "A359082", "A359411", "A359412" ]
null
Amiram Eldar, Dec 30 2022
2023-09-01T11:26:46
oeisdata/seq/A359/A359411.seq
aed553e4c3db26ec43b088de49c60bcd
A359412
Numbers with a record number of divisors that are both infinitary and exponential.
[ "1", "8", "216", "27000", "9261000", "12326391000", "27081081027000", "110924107886592000", "544970142046826496000", "3737950204299182936064000", "45479640135708158783090688000", "1109202943269786284560798789632000", "33044264882950203203350756741926912000", "1673791149116076642859325881248823873536000" ]
[ "nonn" ]
12
1
2
[ "A000079", "A000578", "A025487", "A037992", "A115964", "A318278", "A359411", "A359412" ]
null
Amiram Eldar, Dec 30 2022
2023-04-06T06:35:46
oeisdata/seq/A359/A359412.seq
9d46f0952ff2520cf71eb78cac720eb7
A359413
Triangle read by rows: T(n, k) is the number of permutations of size n that require exactly k iterations of the pop-stack sorting map to reach the identity, for n >= 1, 0 <= k <= n-1.
[ "1", "1", "1", "1", "3", "2", "1", "7", "8", "8", "1", "15", "26", "46", "32", "1", "31", "80", "191", "262", "155", "1", "63", "234", "735", "1440", "1737", "830", "1", "127", "664", "2752", "6924", "12314", "12432", "5106", "1", "255", "1850", "10114", "31928", "73122", "112108", "98156", "35346", "1", "511", "5088", "36564", "145199", "404758", "816401", "1104042", "844038", "272198" ]
[ "nonn", "tabl" ]
28
1
5
[ "A011782", "A224232", "A293774", "A293775", "A293776", "A293784", "A348905", "A359413" ]
null
Bjarki Ágúst Guðmundsson, Dec 30 2022
2022-12-31T11:44:32
oeisdata/seq/A359/A359413.seq
525b3e06d829ba9760653785be8492a3
A359414
Primes prime(k) such that prime(k)^2 + prime(k+1)^2 - 1 is the square of a prime.
[ "7", "11", "23", "109", "211", "1021", "42967", "297779", "125211211", "11673806759" ]
[ "nonn", "more", "less" ]
11
1
1
[ "A160054", "A359414" ]
null
Robert Israel, Dec 30 2022
2023-01-01T02:58:55
oeisdata/seq/A359/A359414.seq
c7aefb5ba279ac8de7c7f0e67e7d7294
A359415
Numbers k such that phi(k) is a 5-smooth number where phi is the Euler totient function.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "24", "25", "26", "27", "28", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "44", "45", "48", "50", "51", "52", "54", "55", "56", "57", "60", "61", "62", "63", "64", "65", "66", "68", "70", "72", "73", "74", "75", "76", "77", "78", "80", "81", "82", "84", "85", "88", "90", "91", "93", "95", "96", "97", "99" ]
[ "nonn", "easy" ]
25
1
2
[ "A000010", "A051037", "A359415" ]
null
Darío Clavijo, Dec 30 2022
2023-09-28T09:19:43
oeisdata/seq/A359/A359415.seq
369fe776bfdb7dcc7289a517981ec6a2
A359416
Write n as 2^m - k, where 2^m is the least power of 2 >= n (0 <= k <= 2^(m-1)-1). For n a power of 2 (k = 0), a(n) = n. For numbers with k > 0, a(n) is the least p*a(k) which has not occurred previously, the count of k being taken from right to left (backwards) from k = 1 at 2^m - 1.
[ "1", "2", "3", "4", "9", "6", "5", "8", "25", "18", "27", "12", "15", "10", "7", "16", "49", "50", "105", "36", "81", "54", "75", "24", "35", "30", "45", "20", "21", "14", "11", "32", "121", "98", "231", "100", "495", "210", "175", "72", "225", "162", "243", "108", "315", "150", "147", "48", "77", "70", "165", "60", "135", "90", "125", "40", "55", "42", "63", "28", "33", "22", "13", "64" ]
[ "nonn" ]
29
1
2
[ "A000027", "A005940", "A122155", "A356886", "A357057", "A359416" ]
null
David James Sycamore, Dec 30 2022
2025-03-24T22:35:46
oeisdata/seq/A359/A359416.seq
7b468d452326c43d467dde141386014a
A359417
Phi-practical numbers (A260653) whose divisors have distinct values of the Euler totient function (A000010).
[ "1", "3", "15", "105", "165", "195", "255", "495", "525", "735", "975", "1155", "1485", "1785", "1815", "1995", "2145", "2415", "2535", "2625", "2805", "3045", "3135", "3255", "3315", "3675", "3705", "3795", "3885", "4305", "4455", "4485", "4515", "4785", "4845", "4875", "4935", "5115", "5145", "5445", "5565", "5655", "5865", "6045", "6105", "6195", "6405" ]
[ "nonn" ]
11
1
2
[ "A000010", "A260653", "A326835", "A359417" ]
null
Amiram Eldar, Dec 31 2022
2023-01-04T01:25:50
oeisdata/seq/A359/A359417.seq
a3bd8ecd51b60fd147b51555c7f5575b
A359418
Unitary phi-practical (A286906) whose unitary divisors have distinct values of the unitary totient function uphi (A047994).
[ "1", "3", "15", "105", "165", "195", "255", "1155", "1785", "1995", "2145", "2415", "2805", "3045", "3135", "3255", "3315", "3705", "3795", "3885", "4305", "4485", "4515", "4785", "4845", "4935", "5115", "5565", "5655", "5865", "6045", "6105", "6195", "6405", "7035", "7095", "7215", "7395", "7455", "7665", "7755", "7905", "7995", "8295", "8385", "8715" ]
[ "nonn" ]
8
1
2
[ "A047994", "A286906", "A348004", "A359417", "A359418" ]
null
Amiram Eldar, Dec 31 2022
2023-01-04T01:29:01
oeisdata/seq/A359/A359418.seq
826fce1dac69eca5e39efc66b3cf8d8e
A359419
Nonsquarefree numbers that are both phi-practical and unitary phi-practical.
[ "12", "60", "84", "120", "132", "156", "240", "420", "660", "780", "840", "924", "1020", "1050", "1092", "1140", "1320", "1380", "1428", "1560", "1596", "1680", "1716", "1740", "1860", "1932", "2040", "2100", "2220", "2244", "2280", "2436", "2460", "2508", "2580", "2604", "2640", "2652", "2760", "2820", "2940", "2964", "3036", "3108", "3120", "3180" ]
[ "nonn" ]
9
1
1
[ "A005117", "A013929", "A260653", "A286906", "A359419" ]
null
Amiram Eldar, Dec 31 2022
2023-01-04T01:31:11
oeisdata/seq/A359/A359419.seq
28e6c61c08c51fd4c9b9bc53663893d6
A359420
Numbers that are both practical (A005153) and phi-practical (A260653).
[ "1", "2", "4", "6", "8", "12", "16", "18", "20", "24", "30", "32", "36", "40", "42", "48", "54", "56", "60", "64", "72", "80", "84", "90", "96", "100", "108", "112", "120", "126", "128", "132", "140", "144", "150", "156", "160", "162", "168", "176", "180", "192", "198", "200", "208", "210", "216", "220", "224", "234", "240", "252", "256", "260", "264", "270", "272", "280", "288" ]
[ "nonn" ]
18
1
2
[ "A000010", "A000203", "A005153", "A260653", "A325781", "A325795", "A359420" ]
null
Amiram Eldar, Dec 31 2022
2024-02-04T03:27:22
oeisdata/seq/A359/A359420.seq
e262797847726d8a5ceaa7a44d009e7b
A359421
a(n) = number of abelian groups of order p^2 - 1, where p = prime(n).
[ "1", "3", "3", "5", "3", "3", "14", "6", "5", "3", "11", "6", "5", "3", "7", "9", "3", "3", "3", "10", "10", "7", "3", "10", "22", "6", "5", "9", "9", "7", "44", "3", "5", "3", "6", "10", "3", "15", "5", "3", "6", "6", "15", "15", "12", "20", "3", "11", "3", "3", "10", "7", "14", "18", "30", "5", "9", "21", "3", "5", "3", "6", "6", "5", "5", "3", "3", "14", "3", "6", "11", "10", "7", "3", "9", "22", "3", "6", "14" ]
[ "nonn" ]
22
1
2
[ "A000040", "A000041", "A000688", "A084920", "A359421" ]
null
Ali Ramsey, Dec 31 2022
2025-02-03T09:37:07
oeisdata/seq/A359/A359421.seq
b17baa194583dc4ee785169f36bb8319
A359422
Dirichlet inverse of A187074, characteristic function of numbers that are neither multiples of 3 nor of the form 4u+2.
[ "1", "0", "0", "-1", "-1", "0", "-1", "-1", "0", "0", "-1", "0", "-1", "0", "0", "0", "-1", "0", "-1", "1", "0", "0", "-1", "0", "0", "0", "0", "1", "-1", "0", "-1", "1", "0", "0", "1", "0", "-1", "0", "0", "1", "-1", "0", "-1", "1", "0", "0", "-1", "0", "0", "0", "0", "1", "-1", "0", "1", "1", "0", "0", "-1", "0", "-1", "0", "0", "1", "1", "0", "-1", "1", "0", "0", "-1", "0", "-1", "0", "0", "1", "1", "0", "-1", "0", "0", "0", "-1", "0", "1", "0", "0", "1", "-1", "0", "1", "1", "0", "0", "1", "0", "-1", "0", "0", "0", "-1", "0", "-1", "1", "0" ]
[ "sign", "mult" ]
17
1
null
[ "A010892", "A156277", "A187074", "A355688", "A355689", "A355690", "A359422" ]
null
Antti Karttunen, Dec 31 2022
2023-01-03T09:21:22
oeisdata/seq/A359/A359422.seq
7cd97672b2d33794bf535d2f17c8f752
A359423
The least common multiple of the arithmetic derivative and the primorial base exp-function.
[ "0", "0", "3", "6", "36", "18", "5", "10", "60", "30", "315", "90", "400", "50", "225", "600", "7200", "450", "2625", "250", "3000", "750", "14625", "2250", "27500", "1250", "1875", "33750", "180000", "11250", "217", "14", "1680", "42", "1197", "252", "420", "70", "105", "1680", "21420", "630", "7175", "350", "8400", "13650", "1575", "3150", "14000", "1750", "7875", "10500", "63000", "15750", "354375", "70000" ]
[ "nonn", "base" ]
10
0
3
[ "A003415", "A016825", "A042965", "A276086", "A327858", "A327864", "A358669", "A359423", "A359424" ]
null
Antti Karttunen, Jan 02 2023
2023-01-02T21:55:50
oeisdata/seq/A359/A359423.seq
7f4d5c7542836e1f359302506de8c353
A359424
The least common multiple of the arithmetic derivative and the primorial base exp-function, reduced modulo 60.
[ "0", "0", "3", "6", "36", "18", "5", "10", "0", "30", "15", "30", "40", "50", "45", "0", "0", "30", "45", "10", "0", "30", "45", "30", "20", "50", "15", "30", "0", "30", "37", "14", "0", "42", "57", "12", "0", "10", "45", "0", "0", "30", "35", "50", "0", "30", "15", "30", "20", "10", "15", "0", "0", "30", "15", "40", "0", "30", "45", "30", "8", "38", "57", "18", "24", "42", "5", "10", "0", "30", "15", "30", "0", "50", "15", "30", "0", "30", "55", "10", "0", "0", "15" ]
[ "nonn", "base", "look" ]
8
0
3
[ "A003415", "A016825", "A042965", "A276086", "A327858", "A327864", "A358669", "A358765", "A359423", "A359424" ]
null
Antti Karttunen, Jan 02 2023
2023-01-02T21:55:55
oeisdata/seq/A359/A359424.seq
1438bfc8a25d7f3fbd67a27ae4639ec4
A359425
Dirichlet convolution of the arithmetic derivative with the primorial base exp-function.
[ "0", "2", "2", "11", "2", "19", "2", "45", "18", "35", "2", "85", "2", "31", "40", "151", "2", "125", "2", "195", "36", "119", "2", "313", "38", "83", "120", "215", "2", "418", "2", "649", "124", "491", "52", "628", "2", "295", "88", "1057", "2", "1046", "2", "1629", "414", "2303", "2", "1777", "38", "1541", "496", "2241", "2", "4424", "140", "6421", "300", "11315", "2", "2048", "2", "83", "1002", "2013", "104", "1864", "2", "2073" ]
[ "nonn", "base", "look" ]
9
1
2
[ "A003415", "A276086", "A347389", "A347959", "A359425" ]
null
Antti Karttunen, Jan 02 2023
2023-01-02T21:55:59
oeisdata/seq/A359/A359425.seq
8c310d38bd1ebf289d2394ddc4deaf63
A359426
a(n) = A342001(A358764(n)).
[ "0", "1", "1", "5", "2", "2", "1", "7", "8", "31", "13", "12", "2", "9", "11", "37", "16", "14", "3", "11", "14", "43", "19", "16", "4", "13", "17", "49", "22", "5", "1", "9", "10", "41", "17", "16", "12", "59", "71", "247", "106", "94", "19", "73", "92", "289", "127", "108", "26", "87", "113", "331", "148", "122", "33", "101", "134", "373", "169", "41", "2", "11", "13", "47", "20", "18", "17", "69", "86", "277", "121", "104", "24", "83", "107" ]
[ "nonn", "base", "look" ]
9
1
4
[ "A276086", "A342001", "A342002", "A358764", "A359426" ]
null
Antti Karttunen, Jan 02 2023
2023-01-02T16:48:29
oeisdata/seq/A359/A359426.seq
71ae8d64550b95fa819b206785249e0a
A359427
Dirichlet inverse of A358764.
[ "1", "-2", "-3", "-2", "-9", "8", "-5", "6", "-6", "6", "-45", "-4", "-25", "-30", "-21", "-130", "-225", "-70", "-125", "-130", "-345", "-570", "-1125", "-480", "-544", "-1150", "-1812", "-3550", "-5625", "222", "-7", "530", "249", "858", "27", "418", "-35", "430", "45", "610", "-315", "1520", "-175", "2650", "-48", "3450", "-1575", "2060", "-850", "804", "-1275", "-250", "-7875", "4288", "-3565", "6150", "-12375" ]
[ "sign", "base" ]
9
1
2
[ "A056911", "A060681", "A276086", "A323239", "A337945", "A342417", "A358764", "A359427", "A359428" ]
null
Antti Karttunen, Jan 02 2023
2023-01-02T16:48:55
oeisdata/seq/A359/A359427.seq
e903e0159dd7e03d2516bdf807693a9e
A359428
Sum of A358764 and its Dirichlet inverse.
[ "2", "0", "0", "4", "0", "12", "0", "16", "9", "36", "0", "16", "0", "20", "54", "20", "0", "30", "0", "120", "30", "180", "0", "20", "81", "100", "63", "200", "0", "228", "0", "544", "270", "900", "90", "446", "0", "500", "150", "820", "0", "1660", "0", "3000", "477", "4500", "0", "2760", "25", "2554", "1350", "5000", "0", "7788", "810", "14900", "750", "22500", "0", "936", "0", "28", "2265", "-12", "450", "3324", "0", "168", "6750" ]
[ "sign", "base", "look" ]
12
1
1
[ "A053850", "A060681", "A276086", "A342419", "A353569", "A358764", "A359427", "A359428" ]
null
Antti Karttunen, Jan 02 2023
2023-01-02T16:48:22
oeisdata/seq/A359/A359428.seq
bfc1e784833c42a5e7c1f818f8c8b37a
A359429
a(n) = 1 if n is cubefree, but not squarefree, otherwise 0.
[ "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "1" ]
[ "nonn" ]
14
1
null
[ "A008966", "A059956", "A067259", "A072411", "A088453", "A107078", "A212793", "A290107", "A359429", "A359474" ]
null
Antti Karttunen, Jan 04 2023
2023-01-05T03:20:32
oeisdata/seq/A359/A359429.seq
edf3dcf971b5fee1a622a339426c6acf
A359430
a(n) = 1 if the arithmetic derivative of n is a multiple of 3, otherwise 0.
[ "1", "1", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "1", "1", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "1", "0", "1", "0", "0", "1", "0", "0", "1", "1" ]
[ "nonn" ]
19
0
null
[ "A003415", "A011655", "A267142", "A276086", "A327863", "A359430", "A369643", "A369653", "A369658", "A370118", "A370122", "A373143", "A373253", "A373254", "A373256", "A373371", "A373591", "A373592" ]
null
Antti Karttunen, Jan 02 2023
2024-06-13T14:57:21
oeisdata/seq/A359/A359430.seq
7a7d9e40b93a2842de384a58924fb499
A359431
a(n) = A325973(n) - A326043(n).
[ "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "4", "0", "0", "2", "0", "0", "0", "0", "5", "0", "0", "0", "3", "0", "0", "0", "6", "0", "0", "0", "0", "0", "0", "0", "8", "0", "0", "0", "0", "0", "6", "0", "8", "0", "0", "0", "0", "0", "0", "0", "12", "0", "0", "0", "0", "0", "0", "0", "16", "0", "0", "0", "0", "0", "0", "0", "12", "12", "0", "0", "0", "0", "0", "0", "12", "0", "0", "0", "0", "0", "0", "0", "20", "0", "0", "0", "10", "0", "0", "0", "14", "0" ]
[ "nonn" ]
8
1
16
[ "A048107", "A325973", "A325981", "A326043", "A359431", "A359471" ]
null
Antti Karttunen, Jan 04 2023
2023-01-04T14:38:13
oeisdata/seq/A359/A359431.seq
acc0c839b5c8210e0f4bccc0ca02ae1b
A359432
Dirichlet inverse of A327936, which is multiplicative sequence with a(p^e) = p if e >= p, otherwise 1.
[ "1", "-1", "-1", "-1", "-1", "1", "-1", "1", "0", "1", "-1", "1", "-1", "1", "1", "1", "-1", "0", "-1", "1", "1", "1", "-1", "-1", "0", "1", "-2", "1", "-1", "-1", "-1", "-1", "1", "1", "1", "0", "-1", "1", "1", "-1", "-1", "-1", "-1", "1", "0", "1", "-1", "-1", "0", "0", "1", "1", "-1", "2", "1", "-1", "1", "1", "-1", "-1", "-1", "1", "0", "-1", "1", "-1", "-1", "1", "1", "-1", "-1", "0", "-1", "1", "0", "1", "1", "-1", "-1", "-1", "2", "1", "-1", "-1", "1", "1", "1", "-1", "-1", "0", "1", "1", "1", "1", "1", "1", "-1", "0", "0", "0", "-1", "-1", "-1", "-1", "-1", "1", "-1", "2" ]
[ "sign", "mult" ]
12
1
27
[ "A038838", "A122132", "A327936", "A353627", "A358216", "A359432", "A359433" ]
null
Antti Karttunen, Jan 02 2023
2023-01-26T04:13:07
oeisdata/seq/A359/A359432.seq
6960b6ccf669fd70ae74c2dfa2b03a4f
A359433
Dirichlet inverse of A071773.
[ "1", "-1", "-1", "-1", "-1", "1", "-1", "1", "-2", "1", "-1", "1", "-1", "1", "1", "1", "-1", "2", "-1", "1", "1", "1", "-1", "-1", "-4", "1", "2", "1", "-1", "-1", "-1", "-1", "1", "1", "1", "2", "-1", "1", "1", "-1", "-1", "-1", "-1", "1", "2", "1", "-1", "-1", "-6", "4", "1", "1", "-1", "-2", "1", "-1", "1", "1", "-1", "-1", "-1", "1", "2", "-1", "1", "-1", "-1", "1", "1", "-1", "-1", "-2", "-1", "1", "4", "1", "1", "-1", "-1", "-1", "4", "1", "-1", "-1", "1", "1", "1", "-1", "-1", "-2", "1", "1", "1", "1", "1", "1", "-1", "6", "2", "4", "-1", "-1", "-1", "-1", "-1" ]
[ "sign", "mult" ]
17
1
9
[ "A038838", "A071773", "A122132", "A353627", "A359432", "A359433" ]
null
Antti Karttunen, Jan 02 2023
2023-01-04T02:09:47
oeisdata/seq/A359/A359433.seq
c18658b2195b8a71d5687db23c6dbe41
A359434
Numbers k >= 1 such that k * phi(k) / (k + phi(k)) is an integer, where phi(k) = A000010(k).
[ "12", "24", "36", "48", "72", "96", "108", "126", "144", "176", "192", "216", "252", "288", "324", "352", "378", "384", "432", "504", "576", "648", "704", "756", "768", "864", "882", "972", "1008", "1134", "1152", "1296", "1408", "1512", "1536", "1728", "1764", "1936", "1944", "2016", "2268", "2304", "2592", "2646", "2752", "2816", "2916" ]
[ "nonn" ]
8
1
1
[ "A000010", "A003586", "A033845", "A359434" ]
null
Ctibor O. Zizka, Dec 31 2022
2022-12-31T15:17:11
oeisdata/seq/A359/A359434.seq
61ff93f82156886e6a02c12c4330119e
A359435
a(n) = binomial(2*n-1,n) - n^2 - 1.
[ "0", "18", "100", "425", "1666", "6370", "24228", "92277", "352594", "1351933", "5200130", "20058103", "77558534", "300539938", "1166802820", "4537567325", "17672631538", "68923264009", "269128936778", "1052049481375", "4116715363270", "16123801840973", "63205303218250", "247959266473375", "973469712823326" ]
[ "nonn", "easy" ]
6
3
2
[ "A352027", "A359435" ]
null
Enrique Navarrete, Dec 31 2022
2024-01-20T16:24:56
oeisdata/seq/A359/A359435.seq
c2b969ba8ba8d4e0d6fe97b769672342
A359436
Primes p such that (4^p - 2^p + 1)/3 is prime.
[ "3", "5", "7", "13", "29", "61", "383", "401", "1637", "1871", "36229", "44771", "44797", "75167" ]
[ "nonn", "more", "hard" ]
28
1
1
[ "A000978", "A359436" ]
null
Jorge Coveiro, Dec 31 2022
2024-09-10T11:53:06
oeisdata/seq/A359/A359436.seq
c5bd05c07c16cf878f960ef904b42109
A359437
a(n) is the first prime p such that there are exactly n numbers i with 1 <= i < p such that one of i*p-(p-i) and i*p+(p-i) is a prime and the other is the square of a prime.
[ "2", "17", "11", "7", "239", "167", "1933", "9241", "19319", "120121", "649991", "4564559", "513239", "11324041", "31831799", "54708721", "59219161", "215975759", "241431959", "265012441", "549789239", "138389159", "3336693359", "1990674841" ]
[ "nonn", "more" ]
36
0
1
null
null
Robert Israel, Dec 31 2022
2024-05-07T02:00:20
oeisdata/seq/A359/A359437.seq
15fb1d29e0fcca69db1029b401c8e462
A359438
For n >= 0, let S be the sequence of numbers m such that (m^2 - 2*n^2 + 1)/2 is a square. Then a(n) is the number k such that S(j) = 6*S(j-k) - S(j-2k) for all j for which S(j-2k) is defined.
[ "1", "1", "2", "2", "2", "3", "2", "2", "2", "4", "2", "2", "4", "2", "4", "2", "4", "2", "2", "4", "4", "2", "2", "4", "2", "2", "4", "4", "2", "3", "4", "4", "4", "4", "2", "4", "2", "8", "2", "2", "4", "2", "2", "2", "6", "2", "2", "4", "4", "2", "2", "4", "2", "4", "8", "4", "2", "4", "6", "2", "4", "4", "2", "2", "2", "8", "4", "4", "4", "2", "4", "4", "4", "2", "4", "4", "2", "4", "4", "4", "2", "2", "8", "4", "4", "2", "4" ]
[ "nonn" ]
6
0
3
[ "A000005", "A001541", "A002315", "A077242", "A077443", "A106525", "A359438" ]
null
Jon E. Schoenfield, Dec 31 2022
2023-01-01T09:48:32
oeisdata/seq/A359/A359438.seq
16c3851dc2b48c2de4c0e8b3367326e4
A359439
a(n) is the least number of the form p^2 + q^2 - 2 for primes p and q that is an odd multiple of 2^n, or -1 if there is no such number.
[ "11", "6", "-1", "56", "16", "32", "192", "128", "2816", "1536", "15360", "30720", "12288", "73728", "147456", "32768", "196608", "1179648", "22806528", "11010048", "34603008", "31457280", "314572800", "679477248", "50331648", "301989888", "1006632960", "10871635968", "20132659200", "4831838208", "28991029248", "173946175488", "450971566080", "77309411328" ]
[ "sign" ]
41
0
1
[ "A045636", "A359439" ]
null
Robert Israel, Jan 02 2023
2023-01-05T19:00:14
oeisdata/seq/A359/A359439.seq
8457216fc4451462ea778664fc47b5b2
A359440
A measure of the extent of reflective symmetry in the pattern of primes around each prime gap: a(n) is the largest k such that prime(n-j) + prime(n+1+j) has the same value for each j in 0..k.
[ "0", "0", "0", "1", "2", "2", "1", "0", "0", "4", "0", "0", "2", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "2", "1", "0", "1", "0", "0", "0", "2", "0", "0", "0", "5", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "1", "0", "0" ]
[ "nonn" ]
45
1
5
[ "A000040", "A006562", "A051795", "A055381", "A081235", "A359440" ]
null
Alexandre Herrera, Jan 01 2023
2023-01-08T13:30:18
oeisdata/seq/A359/A359440.seq
327613427e4cc9be17c5bef729f117d3
A359441
The n-Queens Constant.
[ "1", "9", "4", "4", "0", "0" ]
[ "nonn", "cons", "hard", "more" ]
10
1
2
[ "A000170", "A359441" ]
null
Vaclav Kotesovec, Jan 01 2023
2023-01-01T08:44:01
oeisdata/seq/A359/A359441.seq
01b30a2755a3a5769c68335488fdcd76
A359442
a(n) = Sum_{d|n} d^(n + 1 - d - n/d).
[ "1", "2", "2", "4", "2", "15", "2", "74", "83", "643", "2", "12635", "2", "117715", "397188", "2359426", "2", "103572204", "2", "1260918355", "13841818644", "25937425627", "2", "5612318393211", "152587890627", "23298085126579", "1853020231898564", "2422197090649523", "2", "1032944452284531101", "2", "10376297939508166658" ]
[ "nonn" ]
50
1
2
[ "A294645", "A342628", "A342629", "A342677", "A359442", "A359700" ]
null
Seiichi Manyama, Jan 14 2023
2023-08-09T00:53:37
oeisdata/seq/A359/A359442.seq
a4a4344e0af8982ca882aab27a7a23af
A359443
Primes p such that if q is the next prime, the sum (with multiplicity) of prime factors of p^2 + q^2 is a square.
[ "11", "17", "23", "79", "131", "229", "1019", "1123", "1583", "3299", "4019", "4091", "15307", "28813", "29147", "35083", "35933", "43427", "43597", "47809", "68683", "69029", "72047", "80173", "80513", "82483", "83257", "84263", "92567", "94583", "100693", "118603", "129517", "155317", "163243", "165553", "190181", "191021", "198901", "199211", "223439", "225721", "257273", "265117" ]
[ "nonn" ]
8
1
1
[ "A001414", "A051448", "A359443" ]
null
Robert Israel, Jan 01 2023
2023-01-06T03:24:41
oeisdata/seq/A359/A359443.seq
5e5696e329485bf881dc6eb88aa34766
A359444
a(n) is the least number that has exactly n divisors with sum of digits n.
[ "1", "20", "60", "440", "1400", "420", "11200", "11440", "324", "58520", "180880", "18480", "585200", "523600", "114240", "1133440", "2420600", "17820", "9634240", "9529520", "1659840", "33353320", "71380400", "4748100", "178890320", "228388160", "671328", "413736400", "1081662400", "73670520", "3301916800", "2325202880" ]
[ "nonn", "base" ]
59
1
2
[ "A007953", "A359444", "A359959" ]
null
Robert Israel, Jan 21 2023
2023-01-27T19:57:16
oeisdata/seq/A359/A359444.seq
143d7abeee00f72e4987c3e6fc6714e8
A359445
Numbers k such that the sums (with multiplicity) of prime factors of k and k+1 are both squares.
[ "255", "290", "323", "578", "1484", "2219", "2418", "2491", "4370", "4706", "5243", "6075", "7139", "7930", "9378", "10082", "10554", "10603", "12716", "15872", "16739", "18146", "18938", "22424", "22842", "25227", "25283", "25959", "26910", "28364", "28448", "30255", "33669", "33698", "34316", "34317", "38895", "40179", "41261", "43343", "43999", "47384", "60400", "62695", "64970" ]
[ "nonn" ]
15
1
1
[ "A001414", "A051448", "A359445" ]
null
Robert Israel, Jan 01 2023
2024-04-12T09:25:09
oeisdata/seq/A359/A359445.seq
78fa45844d5ee0ea77ea8da781ee2d98
A359446
a(n) is the period of the decimal expansion of 1/A243110(n).
[ "1", "2", "3", "4", "7", "5", "21", "29", "20", "22", "7", "10", "11", "18", "35", "51", "45", "61", "9", "11", "14", "17", "15", "16", "21", "47", "51", "54", "55", "24", "28", "37", "13", "44", "44", "26", "17" ]
[ "nonn", "base", "more" ]
23
1
2
[ "A060370", "A243110", "A359446" ]
null
Pedro K. Krause, Jan 01 2023
2023-02-26T20:34:03
oeisdata/seq/A359/A359446.seq
84ea172728d3f3e4a3bcc49409356ac7
A359447
a(n) is the least number that is the sum of two cubes of primes and is 2^n times an odd prime, or -1 if there is no such number.
[ "-1", "-1", "152", "2224", "9056", "108736", "-1", "4532992", "34674176", "268684288", "2280249344", "18693763072", "138890141696", "1111848828928", "8803419521024", "70375767212032", "564861779443712", "4507018424221696", "36030079546425344", "288238419152207872", "2305850719072157696", "18446757709572210688", "147573952867129622528" ]
[ "sign" ]
10
1
3
[ "A086119", "A359447", "A359448" ]
null
Robert Israel, Jan 01 2023
2023-01-06T10:43:43
oeisdata/seq/A359/A359447.seq
ad5358ec1fa165bfefee9629ee99bb0b
A359448
a(n) is the least number that is the sum of two cubes of primes and is 2^n times an odd number.
[ "35", "54", "468", "152", "16", "9056", "81088", "527744", "4532992", "33900032", "268684288", "2148866048", "17185288192", "137439174656", "1099611160576", "8797884612608", "70369850097664", "562950041894912", "4503607335190528", "36028810622664704", "288230406982991872", "2305843633483415552", "18446744212436156416", "147573952867129622528" ]
[ "nonn" ]
15
0
1
[ "A007814", "A086119", "A359447", "A359448" ]
null
Robert Israel, Jan 01 2023
2024-07-09T19:12:25
oeisdata/seq/A359/A359448.seq
3dfb04c23bb9d7d1fed42f8e7244eaf3
A359449
Positive integers in which the sum of the k-th powers of their digits is a prime number for k = 1, 2, 3, 4, 5, and 6 but not for k=7.
[ "223", "232", "322", "1349", "1394", "1439", "1493", "1934", "1943", "2023", "2032", "2203", "2230", "2302", "2320", "3022", "3149", "3194", "3202", "3220", "3419", "3491", "3914", "3941", "4139", "4193", "4319", "4391", "4913", "4931", "9134", "9143", "9314", "9341", "9413", "9431", "10349", "10394", "10439", "10493", "10934", "10943", "13049", "13094", "13409", "13490", "13904", "13940" ]
[ "nonn", "base", "easy" ]
25
1
1
[ "A028834", "A108662", "A210767", "A225534", "A245358", "A359449" ]
null
José Hernández, Jan 02 2023
2023-01-20T10:00:54
oeisdata/seq/A359/A359449.seq
aaf0aa91c720972d912c37e63ee4614a
A359450
a(1) = 1, a(2) = 2; thereafter a(n) = n * a(A070939(n)).
[ "1", "2", "6", "24", "30", "36", "42", "192", "216", "240", "264", "288", "312", "336", "360", "480", "510", "540", "570", "600", "630", "660", "690", "720", "750", "780", "810", "840", "870", "900", "930", "1152", "1188", "1224", "1260", "1296", "1332", "1368", "1404", "1440", "1476", "1512", "1548", "1584", "1620", "1656", "1692", "1728", "1764", "1800", "1836" ]
[ "nonn", "base" ]
11
1
2
[ "A070939", "A359450", "A359451" ]
null
Amiram Eldar, Jan 02 2023
2023-01-04T01:30:58
oeisdata/seq/A359/A359450.seq
d47552d507c3ec4abaffdafebf8452f2
A359451
Decimal expansion of Sum_{k>=1} 1/A359450(k).
[ "2", "0", "8", "6", "3", "7", "7", "6", "6", "5", "0", "0", "5", "9", "8", "8", "7", "1", "6", "0", "8", "9", "7", "5", "5", "8", "5", "6", "7", "3", "4", "1", "3", "2", "7", "7", "2", "6", "9", "2", "0", "2", "2", "0", "9", "6", "9", "2", "2", "3", "9", "5", "1", "6", "9", "5", "1", "2", "3", "8", "3", "8", "5", "7", "9", "2", "1", "5", "3", "2", "0", "0", "0", "2", "8", "2", "1", "0", "0", "2", "6", "1", "4", "7", "1", "6", "0", "5", "8", "4", "8", "5", "2", "6", "7", "0", "9", "4", "9", "0", "7" ]
[ "nonn", "cons", "base" ]
10
1
1
[ "A001008", "A002805", "A359450", "A359451" ]
null
Amiram Eldar, Jan 02 2023
2025-03-24T22:35:55
oeisdata/seq/A359/A359451.seq
bc28235a413ca86a39783ada6588db68
A359452
Number of vertices in the partite set of the n-Menger sponge graph that contains the corners.
[ "1", "8", "208", "3968", "80128", "1599488", "32002048", "639991808", "12800032768", "255999868928", "5120000524288", "102399997902848", "2048000008388608", "40959999966445568", "819200000134217728", "16383999999463129088", "327680000002147483648", "6553599999991410065408", "131072000000034359738368" ]
[ "nonn", "easy" ]
27
0
2
[ "A009964", "A083233", "A262710", "A291066", "A332705", "A359452", "A359453" ]
null
Allan Bickle, Jan 02 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359452.seq
c5a0a366144318476247fb0b94602ba5
A359453
Number of vertices in the partite set of the n-Menger sponge graph that do not contain the corners.
[ "0", "12", "192", "4032", "79872", "1600512", "31997952", "640008192", "12799967232", "256000131072", "5119999475712", "102400002097152", "2047999991611392", "40960000033554432", "819199999865782272", "16384000000536870912", "327679999997852516352", "6553600000008589934592", "131071999999965640261632" ]
[ "nonn", "easy" ]
27
0
2
[ "A009964", "A083233", "A291066", "A332705", "A359452", "A359453" ]
null
Allan Bickle, Jan 02 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359453.seq
8ea4267a639362ba0cc2e5ea34bc0a52
A359454
Decimal expansion of Knopfmacher's limit: Limit_{x -> 1 from below} (1/(1-x)) * Product_{k>=2} (1 - x^m(k)/(k+1)), where m(k) = A060681(k) = k - k/A020639(k).
[ "2", "2", "9", "2", "1", "7", "3", "6", "9", "5", "3" ]
[ "nonn", "cons", "more" ]
5
1
1
[ "A020639", "A060681", "A359454" ]
null
Amiram Eldar, Jan 02 2023
2023-01-02T03:32:44
oeisdata/seq/A359/A359454.seq
953e228d946ac4505a6666088da4eb5e
A359455
Expansion of Sum_{k>0} x^k / (1 - x^(k^3)).
[ "1", "2", "2", "2", "2", "2", "2", "2", "2", "3", "2", "2", "2", "2", "2", "2", "2", "3", "2", "2", "2", "2", "2", "2", "2", "3", "2", "2", "2", "3", "2", "2", "2", "3", "2", "2", "2", "2", "2", "2", "2", "3", "2", "2", "2", "2", "2", "2", "2", "3", "2", "2", "2", "2", "2", "2", "3", "3", "2", "2", "2", "2", "2", "2", "2", "3", "2", "3", "2", "2", "2", "2", "2", "3", "2", "2", "2", "2", "2", "2", "2", "3", "2", "3", "2", "2", "2", "2", "2", "3", "2", "2", "2", "2", "2", "2", "2", "3", "2", "2" ]
[ "nonn", "easy" ]
33
1
2
[ "A000005", "A163671", "A359455" ]
null
Seiichi Manyama, Jan 06 2023
2023-08-14T01:59:28
oeisdata/seq/A359/A359455.seq
16aa0e8559f1f399b6bc06b6e2728d72
A359456
Characteristic function of Fibonorial numbers.
[ "1", "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", "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", "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", "cons", "easy" ]
40
1
null
[ "A003266", "A012245", "A359456" ]
null
A.H.M. Smeets, Jan 02 2023
2024-12-15T17:14:49
oeisdata/seq/A359/A359456.seq
b2de01d209008673910aa3d4bd7cfaa3
A359457
Continued fraction for constant A359456.
[ "0", "9", "11", "99", "1", "10", "9", "999999999999999999", "1", "8", "10", "1", "99", "11", "9" ]
[ "nonn", "cofr", "more" ]
24
0
2
[ "A058304", "A317331", "A317332", "A317333", "A359456", "A359457", "A359458" ]
null
A.H.M. Smeets, Jan 02 2023
2025-03-24T22:36:01
oeisdata/seq/A359/A359457.seq
87fb6b3167ece61cb741997b49037a8d
A359458
a(n) = A001911(n)*A003266(n+2).
[ "0", "2", "18", "180", "2640", "59280", "2096640", "118067040", "10659448800", "1548438091200", "362727075110400", "137200338475200000", "83862700757150515200", "82876486430812314240000", "132456397879190606981760000", "342431262483097194433458432000", "1432128704666605129972385934336000" ]
[ "nonn", "easy" ]
21
0
2
[ "A000045", "A001911", "A003266", "A359456", "A359457", "A359458" ]
null
A.H.M. Smeets, Jan 03 2023
2023-02-20T13:05:46
oeisdata/seq/A359/A359458.seq
779e5b3a92ef720f24816e89b1488bbc
A359459
a(n) = coefficient of x^n/n! in A(x) = Sum_{n>=0} x^n/n! * ( (1 + sqrt(n)*x)^sqrt(n) + 1/(1 - sqrt(n)*x)^sqrt(n) )/2.
[ "1", "1", "3", "10", "49", "331", "3091", "36142", "507585", "8264917", "153670771", "3217628206", "75150452257", "1941092955127", "55052488501011", "1703811095028946", "57225901450900801", "2075951065582081417", "80989170394085892451", "3385153152861566082994", "151069646253007978014801", "7176064437477333753215491" ]
[ "nonn" ]
18
0
3
null
null
Paul D. Hanna, Jan 03 2023
2023-01-07T10:53:02
oeisdata/seq/A359/A359459.seq
1a3cdb7d9caa5da4103b8e6a0a2ab92e
A359460
a(n) = coefficient of x^n/n! in A(x) = Sum_{n>=0} x^n * ( (exp(sqrt(n)*x) + x)^sqrt(n) + exp(n*x)/(1 + x*exp(sqrt(n)*x))^sqrt(n) )/2.
[ "1", "1", "4", "18", "124", "1015", "10446", "124894", "1734160", "27065133", "473544010", "9079863496", "190885380192", "4332022328803", "106201585772114", "2781910780856250", "77941165007299936", "2315379935517658841", "73009619250079314690", "2426165226652313377828", "85041434421474110745040" ]
[ "sign" ]
10
0
3
[ "A359460", "A359461" ]
null
Paul D. Hanna, Jan 02 2023
2023-01-03T09:21:15
oeisdata/seq/A359/A359460.seq
2b20bfd63412d607b48a169f89d22b8b
A359461
a(n) = coefficient of x^n/n! in A(x) such that A(x) = Sum_{n>=0} x^n * ( (A(x)^sqrt(n) + x)^sqrt(n) + A(x)^n/(1 + x*A(x)^sqrt(n))^sqrt(n) )/2.
[ "1", "1", "4", "27", "264", "3480", "57960", "1168860", "27716080", "755797392", "23309811000", "802356730560", "30495894175296", "1268569374923136", "57327261461502032", "2796658399257297120", "146484112541333548800", "8199099498574437696000", "488395687438426037605920", "30847715523237047711124096", "2059258090155754103465678080" ]
[ "nonn" ]
23
0
3
[ "A359460", "A359461", "A359462" ]
null
Paul D. Hanna, Jan 02 2023
2023-01-05T00:12:31
oeisdata/seq/A359/A359461.seq
e2abed7ea5f59f655a99b1d9cc7ad0e2
A359462
a(n) = coefficient of x^n/n! in A(x) = Sum_{n>=0} x^n * ( (A(x)^sqrt(2*n) + x)^sqrt(2*n) + A(x)^(2*n)/(1 + x*A(x)^sqrt(2*n))^sqrt(2*n) )/2.
[ "1", "1", "6", "66", "1080", "24210", "689160", "23806160", "967458688", "45226555164", "2391009969600", "141058577704968", "9187128380964864", "654761426765669080", "50687036874968329472", "4235395789572088071840", "379953548646431877841920", "36422572996966918108870800", "3715607345159938499844931584" ]
[ "nonn" ]
6
0
3
[ "A359461", "A359462" ]
null
Paul D. Hanna, Jan 03 2023
2023-01-05T10:34:30
oeisdata/seq/A359/A359462.seq
1e642f0a9122c3bac92dd62d3895f2da
A359463
Coefficient a(n) of x^n in power series A(x), n >= 0, such that A(x) = Sum_{n=-oo..+oo} (-x*A(x))^n * (1 - (-x*A(x))^(n-1))^n.
[ "1", "1", "2", "6", "20", "69", "245", "896", "3362", "12869", "50024", "196896", "783205", "3143713", "12717532", "51798089", "212233756", "874193355", "3617797596", "15035379576", "62724649455", "262579756558", "1102680011825", "4643936681122", "19609621413193", "83005706694022", "352145760387515", "1497067760933244" ]
[ "nonn" ]
11
0
3
[ "A290003", "A359463" ]
null
Paul D. Hanna, Jan 17 2023
2023-03-14T04:20:58
oeisdata/seq/A359/A359463.seq
4f23af1fafbf79cf2c7e216b6965980c
A359464
a(n) = 1 if the total number of 1-bits in the exponents of prime factorization n is even, otherwise 0.
[ "1", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "1", "0", "0", "1", "0", "1", "1", "1", "0", "0", "0", "1", "1", "1", "0", "0", "0", "1", "1", "1", "1", "1", "0", "1", "1", "0", "0", "0", "0", "1", "1", "1", "0", "1", "0", "1", "1", "1", "0", "0", "1", "0", "1", "1", "0", "0", "0", "1", "1", "1", "1", "0", "0", "1", "1", "0", "0", "0", "0", "1", "1", "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "1", "0", "0", "0", "1", "1", "1", "1", "1", "0", "0", "1", "1", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "1", "1", "1", "1", "1", "1" ]
[ "nonn", "easy", "base" ]
24
1
null
[ "A000379", "A059841", "A064547", "A092248", "A359464", "A359465", "A367514" ]
null
Antti Karttunen, Jan 02 2023
2024-10-02T12:36:06
oeisdata/seq/A359/A359464.seq
c022879bea6cdc9f65bdd20729f80de7
A359465
a(n) = 1 if n is an odd squarefree number with an even number of prime factors, otherwise 0.
[ "1", "0", "0", "0", "0", "0", "0", "0", "0", "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", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "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", "0" ]
[ "nonn" ]
16
1
null
[ "A000035", "A008966", "A046390", "A056913", "A065043", "A185197", "A323239", "A343370", "A353481", "A353557", "A353629", "A353675", "A359464", "A359465" ]
null
Antti Karttunen, Jan 02 2023
2023-01-05T03:20:19
oeisdata/seq/A359/A359465.seq
53aab9a859533ec5b439efb39efc4979
A359466
a(n) = 1 if n has exactly one non-unitary prime factor, otherwise 0.
[ "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "1", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "1", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1" ]
[ "nonn" ]
18
1
null
[ "A056170", "A059956", "A154945", "A181819", "A190641", "A353670", "A359466", "A359467", "A359472", "A359474" ]
null
Antti Karttunen, Jan 02 2023
2023-01-05T03:20:28
oeisdata/seq/A359/A359466.seq
d6367683d3a172eda609197afafcfe7a
A359467
a(n) = (A166486(n)+A353627(n)) mod 2.
[ "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "1", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "1", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1" ]
[ "nonn" ]
21
1
null
[ "A166486", "A342419", "A353459", "A353627", "A355689", "A358839", "A359466", "A359467", "A359468", "A359469" ]
null
Antti Karttunen, Jan 02 2023
2023-01-24T02:50:51
oeisdata/seq/A359/A359467.seq
c0caa9b10c820bd00cce78aeab6a48a7
A359468
Numbers that are either multiples of 4 with their odd part squarefree, or that are not multiples of 4 and not squarefree.
[ "4", "8", "9", "12", "16", "18", "20", "24", "25", "27", "28", "32", "40", "44", "45", "48", "49", "50", "52", "54", "56", "60", "63", "64", "68", "75", "76", "80", "81", "84", "88", "90", "92", "96", "98", "99", "104", "112", "116", "117", "120", "121", "124", "125", "126", "128", "132", "135", "136", "140", "147", "148", "150", "152", "153", "156", "160", "162", "164", "168", "169", "171", "172", "175", "176", "184", "188", "189", "192", "198", "204", "207", "208", "212", "220", "224", "225", "228" ]
[ "nonn" ]
18
1
1
[ "A000265", "A166486", "A190641", "A327877", "A342419", "A355689", "A359467", "A359468" ]
null
Antti Karttunen, Jan 02 2023
2023-01-24T02:50:55
oeisdata/seq/A359/A359468.seq
3c2986e20c4fceafc807ceb58735c504
A359469
a(n) = A353459(n) mod 2.
[ "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "1", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "1", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "1" ]
[ "nonn" ]
12
1
null
[ "A003961", "A348717", "A353457", "A353458", "A353459", "A359466", "A359467", "A359469", "A359470" ]
null
Antti Karttunen, Jan 04 2023
2023-01-06T10:51:29
oeisdata/seq/A359/A359469.seq
d1877627d5186b0da38018a447916548
A359470
Positions of odd terms in A353459.
[ "4", "8", "9", "12", "16", "18", "20", "24", "25", "27", "28", "32", "40", "44", "45", "48", "49", "50", "52", "54", "56", "60", "63", "64", "68", "75", "76", "80", "81", "84", "88", "90", "92", "96", "98", "99", "100", "104", "112", "116", "117", "120", "121", "124", "125", "126", "128", "132", "135", "136", "140", "147", "148", "150", "152", "153", "156", "160", "162", "164", "168", "169", "171", "172", "175", "176", "184", "188", "189" ]
[ "nonn" ]
4
1
1
[ "A353459", "A359469", "A359470" ]
null
Antti Karttunen, Jan 04 2023
2023-01-04T12:50:53
oeisdata/seq/A359/A359470.seq
419ef153ebdefe422290106d451fdebb
A359471
a(n) = 1 if the product of exponents in the prime factorization of n is less than 3, otherwise 0.
[ "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "0", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1" ]
[ "nonn" ]
20
1
null
[ "A005361", "A008966", "A034444", "A048105", "A048106", "A048107", "A059956", "A271971", "A325973", "A326043", "A359431", "A359471", "A359472", "A359474", "A359475" ]
null
Antti Karttunen, Jan 04 2023
2023-01-05T03:20:11
oeisdata/seq/A359/A359471.seq
3263468eb28d747dd8b30ddae53f6fca
A359472
a(n) = 1 if the product of exponents in the prime factorization of n is 3, otherwise 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", "0", "0", "1", "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", "1", "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", "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", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1" ]
[ "nonn" ]
26
1
null
[ "A000688", "A005361", "A034444", "A048105", "A048106", "A048109", "A295316", "A295883", "A359466", "A359471", "A359472", "A359473", "A359474" ]
null
Antti Karttunen, Jan 04 2023
2023-01-05T03:20:14
oeisdata/seq/A359/A359472.seq
3f1aea42868c44f6fad9d4c37ec15e30
A359473
a(n) = 1 if the number of divisors of n is a power of 2, otherwise 0.
[ "1", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "0", "1", "0", "1", "0", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "0", "1", "1", "1", "0", "1", "0", "0", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "0", "1", "1", "1" ]
[ "nonn" ]
17
1
null
[ "A000005", "A036537", "A162643", "A209229", "A295316", "A327839", "A348341", "A359472", "A359473" ]
null
Antti Karttunen, Jan 04 2023
2023-01-05T03:20:07
oeisdata/seq/A359/A359473.seq
e798cab73ad78b152c0a2e7df2eb60cb
A359474
a(n) = 1 if the product of exponents in the prime factorization of n is 2, otherwise 0.
[ "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "1" ]
[ "nonn" ]
17
1
null
[ "A000688", "A005361", "A008966", "A046660", "A060687", "A271971", "A302048", "A359429", "A359466", "A359471", "A359472", "A359474", "A359475" ]
null
Antti Karttunen, Jan 04 2023
2023-01-05T03:20:04
oeisdata/seq/A359/A359474.seq
50e709a0fa824ac37fbefc00090347cc
A359475
a(n) = 1 if n is a cubefree nonsquare whose factorization into a product of primes contains exactly one square, otherwise 0.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "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", "1", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0" ]
[ "nonn" ]
14
1
null
[ "A049240", "A072357", "A271971", "A302048", "A359471", "A359474", "A359475" ]
null
Antti Karttunen, Jan 04 2023
2023-01-05T03:19:58
oeisdata/seq/A359/A359475.seq
a96e7c7696a617a43f6ecc4f278086e7
A359476
The sequence {-a(n)}_{n>=1} gives all negative integers that are properly represented by each primitive binary quadratic forms of discriminant 28 that is properly equivalent to the reduced principal form [1, 4, -3].
[ "3", "6", "7", "14", "19", "27", "31", "38", "47", "54", "59", "62", "63", "83", "87", "94", "103", "111", "118", "126", "131", "139", "159", "166", "167", "171", "174", "199", "203", "206", "222", "223", "227", "243", "251", "259", "262", "271", "278", "279", "283", "307", "311", "318", "327", "334", "339", "342", "367", "371", "383", "398", "399", "406", "411", "419", "423", "439", "446", "447", "454", "467", "479", "486" ]
[ "nonn" ]
11
1
1
[ "A242666", "A358946", "A358947", "A359476", "A359477" ]
null
Wolfdieter Lang, Jan 10 2023
2023-04-21T12:49:39
oeisdata/seq/A359/A359476.seq
ad503d73a4467b59a0ee26e9f275541a
A359477
a(n) = 2^m(n), where m(n) is the number of distinct primes, neither 2 nor 7, dividing A359476(n).
[ "2", "2", "1", "1", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "4", "2", "2", "4", "2", "2", "2", "2", "4", "2", "2", "4", "4", "2", "2", "2", "4", "2", "2", "2", "2", "2", "2", "2", "2", "4", "2", "2", "2", "4", "4", "2", "4", "4", "2", "2", "2", "2", "4", "2", "4", "2", "4", "2", "2", "4", "2", "2", "2", "2", "2", "2", "2", "2", "4", "2", "4", "4", "2", "2", "2", "4", "2", "4", "2", "2", "2", "2", "2", "2", "4", "4", "4", "2", "4" ]
[ "nonn" ]
7
1
1
[ "A358946", "A358947", "A359476", "A359477" ]
null
Wolfdieter Lang, Jan 10 2023
2023-01-12T01:53:44
oeisdata/seq/A359/A359477.seq
80d7f449c8494ba0014260a2e534618d
A359478
a(1) = 1; a(n) = -Sum_{k=2..n} k * a(floor(n/k)).
[ "1", "-2", "-5", "-3", "-8", "1", "-6", "-6", "-6", "9", "-2", "-8", "-21", "0", "15", "15", "-2", "-2", "-21", "-31", "-10", "23", "0", "0", "0", "39", "39", "25", "-4", "-49", "-80", "-80", "-47", "4", "39", "39", "2", "59", "98", "98", "57", "-6", "-49", "-71", "-71", "-2", "-49", "-49", "-49", "-49", "2", "-24", "-77", "-77", "-22", "-22", "35", "122", "63", "93", "32", "125", "125", "125", "190", "91" ]
[ "sign", "look" ]
30
1
2
[ "A092149", "A359478", "A359479", "A359484", "A360390", "A360658" ]
null
Seiichi Manyama, Mar 31 2023
2023-05-10T04:30:49
oeisdata/seq/A359/A359478.seq
75a11e076f86bb3f2e3d72e95aafef16
A359479
a(1) = 1; a(n) = Sum_{k=2..n} (-1)^k * k * a(floor(n/k)).
[ "1", "2", "-1", "5", "0", "-3", "-10", "14", "14", "9", "-2", "-20", "-33", "-40", "-25", "71", "54", "54", "35", "5", "26", "15", "-8", "-80", "-80", "-93", "-93", "-135", "-164", "-149", "-180", "204", "237", "220", "255", "255", "218", "199", "238", "118", "77", "98", "55", "-11", "-11", "-34", "-81", "-369", "-369", "-369", "-318", "-396", "-449", "-449", "-394", "-562", "-505", "-534" ]
[ "sign", "look" ]
27
1
2
[ "A309288", "A359479" ]
null
Seiichi Manyama, Mar 31 2023
2023-05-10T04:30:57
oeisdata/seq/A359/A359479.seq
6633516e5082995448d0e786db84bf56
A359480
Number of Q-isomorphism classes of elliptic curves E/Q with good reduction away from 2 and prime(n).
[ "24", "752", "280", "288", "232", "336", "256", "336", "256", "296", "280", "240", "176", "168", "136", "296", "304", "176", "112", "288", "136", "304", "176", "192", "152", "216", "104", "240", "160", "144", "280", "160", "152", "168", "112", "128", "136", "232", "144", "184", "128", "152", "80", "88", "112", "112", "112", "280", "112", "288", "160", "120", "168", "112", "224", "112", "120", "112", "136" ]
[ "nonn" ]
19
1
1
[ "A332545", "A359480", "A361661" ]
null
Robin Visser, Mar 31 2023
2023-06-23T03:30:53
oeisdata/seq/A359/A359480.seq
c3bb911042c1c043bdf85d33f92449dc
A359481
Irregular triangle read by rows in which T(n,k) is one half of the number of overpartitions of n having k distinct parts, n>=1, k>=1.
[ "1", "2", "2", "2", "3", "4", "2", "10", "4", "12", "4", "2", "22", "8", "4", "26", "20", "3", "34", "40", "4", "44", "60", "8", "2", "54", "100", "16", "6", "58", "148", "40", "2", "74", "208", "80", "4", "88", "268", "160", "4", "88", "388", "240", "16", "5", "110", "468", "416", "32", "2", "118", "616", "616", "80", "6", "136", "736", "936", "160", "2", "142", "940", "1296", "320", "6", "162", "1108", "1816", "576" ]
[ "nonn", "tabf" ]
20
1
2
[ "A000005", "A000079", "A000217", "A003056", "A014968", "A116608", "A235790", "A359481" ]
null
Omar E. Pol, Mar 31 2023
2023-06-11T11:50:53
oeisdata/seq/A359/A359481.seq
25b5502ae112d0c588e63b77619125be
A359482
Lexicographically earliest sequence of distinct terms > 0 such that the sum a(n) + a(n+1) is a substring of the concatenation (a(n), a(n+1)).
[ "1", "10", "99", "889", "8009", "1101", "9089", "80718", "100284", "183899", "206021", "396118", "215703", "354632", "108578", "469891", "229021", "61195", "34146", "7321", "13817", "3536", "1825", "749", "167", "508", "324", "2096", "4337", "2958", "2870", "4171", "12941", "16470", "30560", "25465", "21056", "35296", "17665", "35927", "23345", "10106", "548", "279", "516", "1094", "3228", "5302" ]
[ "base", "nonn" ]
45
1
2
[ "A300000", "A359482" ]
null
Eric Angelini and Hans Havermann, Jul 03 2023
2023-08-02T11:50:50
oeisdata/seq/A359/A359482.seq
7af35b86135726cdf9a68e7cbc5c34e1
A359483
For n > 2, a(n) is the least prime p > a(n-1) such that a(n-1) + p is divisible by a(n-2); a(1) = 2, a(2) = 3.
[ "2", "3", "5", "7", "13", "29", "101", "131", "677", "2467", "5657", "19013", "48871", "521519", "553643", "3618509", "14098067", "116168257", "193989217", "1200029867", "8887409417", "12713128189", "573855893333", "773735694701", "9555670385293", "30678585739159", "160434821966701", "1312137293512931", "2217428789754491", "100129280104254127" ]
[ "nonn" ]
12
1
1
null
null
Zak Seidov and Robert Israel, Mar 31 2023
2023-04-02T08:39:37
oeisdata/seq/A359/A359483.seq
7d316ba9c4737dfae2fe985f4bf8caa6
A359484
a(n) = n * mu(n) if n is odd, otherwise n * mu(n) - (n/2) * mu(n/2).
[ "1", "-3", "-3", "2", "-5", "9", "-7", "0", "0", "15", "-11", "-6", "-13", "21", "15", "0", "-17", "0", "-19", "-10", "21", "33", "-23", "0", "0", "39", "0", "-14", "-29", "-45", "-31", "0", "33", "51", "35", "0", "-37", "57", "39", "0", "-41", "-63", "-43", "-22", "0", "69", "-47", "0", "0", "0", "51", "-26", "-53", "0", "55", "0", "57", "87", "-59", "30", "-61", "93", "0", "0", "65", "-99", "-67", "-34", "69", "-105", "-71", "0" ]
[ "sign", "mult" ]
32
1
2
[ "A008683", "A055615", "A092673", "A358276", "A359478", "A359484", "A359485", "A359531" ]
null
Seiichi Manyama, Mar 31 2023
2023-06-09T23:59:03
oeisdata/seq/A359/A359484.seq
c02147c1bef7b7e05b9d0d2d8d2c6a4b
A359485
a(1) = 1, a(2) = -5; a(n) = -n^2 * Sum_{d|n, d < n} a(d) / d^2.
[ "1", "-5", "-9", "4", "-25", "45", "-49", "0", "0", "125", "-121", "-36", "-169", "245", "225", "0", "-289", "0", "-361", "-100", "441", "605", "-529", "0", "0", "845", "0", "-196", "-841", "-1125", "-961", "0", "1089", "1445", "1225", "0", "-1369", "1805", "1521", "0", "-1681", "-2205", "-1849", "-484", "0", "2645", "-2209", "0", "0", "0", "2601", "-676", "-2809", "0", "3025", "0", "3249", "4205", "-3481", "900", "-3721", "4805", "0" ]
[ "sign", "mult" ]
21
1
2
[ "A092673", "A334657", "A359484", "A359485", "A359531", "A360390" ]
null
Seiichi Manyama, Apr 01 2023
2023-05-10T04:31:04
oeisdata/seq/A359/A359485.seq
e0cfe6e11a5677bd2cb79a7f08da895a
A359486
Indices of primes in A087712.
[ "3", "4", "5", "10", "11", "15", "17", "20", "31", "34", "41", "45", "46", "59", "60", "67", "69", "75", "80", "82", "83", "85", "90", "93", "102", "109", "119", "127", "136", "153", "155", "157", "170", "179", "191", "205", "206", "207", "211", "221", "230", "236", "241", "246", "249", "253", "254", "272", "276", "277", "283", "295", "309", "314", "322", "327", "328", "331", "332", "334", "345" ]
[ "nonn" ]
10
1
1
[ "A027746", "A049084", "A087712", "A098282", "A112798", "A359486" ]
null
Jean-Marc Rebert, Jan 02 2023
2023-01-28T11:52:18
oeisdata/seq/A359/A359486.seq
d8b20cd634219ed71373f5940c23440c
A359487
a(n) is the smallest start of a run of 2 or more integers having a prime factor greater than n.
[ "2", "5", "10", "10", "13", "13", "22", "22", "22", "22", "37", "37", "37", "37", "37", "37", "37", "37", "46", "46", "46", "46", "58", "58", "58", "58", "58", "58", "61", "61", "73", "73", "73", "73", "73", "73", "82", "82", "82", "82", "106", "106", "106", "106", "106", "106", "106", "106", "106", "106", "106", "106", "157", "157", "157", "157", "157", "157", "157", "157", "157", "157", "157", "157", "157", "157", "157" ]
[ "nonn" ]
34
1
1
[ "A006530", "A327909", "A359487", "A359488" ]
null
Thomas Garrison, Jan 02 2023
2023-03-28T07:59:43
oeisdata/seq/A359/A359487.seq
f2587fa6774ad38d4ecb5d717a5a4b29
A359488
Run lengths of A359487.
[ "1", "1", "2", "2", "4", "8", "4", "6", "2", "6", "4", "12", "26", "4", "6", "8", "16", "18", "8", "18", "16", "6", "12", "8", "12", "18", "4", "6", "12", "20", "10", "12", "14", "24", "6", "22", "8", "12", "40", "12", "8", "4", "48", "8", "10", "38", "30", "16", "8", "6", "12", "22", "12", "6", "2", "22", "8", "28", "8", "16", "18", "48", "2", "18", "48", "34", "26", "16", "14", "30", "12", "4", "6" ]
[ "nonn" ]
10
1
3
[ "A359487", "A359488" ]
null
Thomas Garrison, Jan 02 2023
2023-02-12T10:39:36
oeisdata/seq/A359/A359488.seq
dcaf70030fc418174c0bdf0dae264e40
A359489
Expansion of 1/sqrt(1 - 4*x/(1-x)^3).
[ "1", "2", "12", "68", "396", "2358", "14262", "87252", "538440", "3345434", "20899816", "131154264", "826135794", "5220372274", "33077821314", "210087769632", "1337104370320", "8525602760550", "54449281992528", "348250972411252", "2230296171922008", "14300414859019290", "91791793780179790" ]
[ "nonn" ]
28
0
2
[ "A085362", "A110170", "A162478", "A359489", "A359758", "A360132" ]
null
Seiichi Manyama, Mar 24 2023
2023-08-09T13:13:24
oeisdata/seq/A359/A359489.seq
9553e86561ee1a80e44e8fad67b85ee6
A359490
Primes p followed by two or more 2-pseudoprimes (A001567) before the next prime.
[ "4363", "13729", "31607", "6973007", "208969199" ]
[ "nonn", "more" ]
11
1
1
[ "A001567", "A335326", "A359490" ]
null
Charles R Greathouse IV, Mar 07 2023
2023-03-13T06:00:58
oeisdata/seq/A359/A359490.seq
cdc29dec4b7a3ab50f89cbdb4bed754b
A359491
Numbers k with the property that the set of decimal digits of k matches the set of first digits of the prime factors of k.
[ "2", "3", "5", "7", "333", "23532", "33165", "77322", "175175", "232152", "321372", "373212", "515375", "712236", "2249232", "2321232", "2971332", "3372138", "3611322", "4313331", "5773131", "12322332", "23147124", "42323112", "72325232", "113338575", "123221232", "132232224", "172232112", "212322912", "221437272", "273233331" ]
[ "nonn", "base" ]
26
1
1
[ "A115024", "A359491" ]
null
John R Phelan, Jan 02 2023
2023-01-28T15:46:49
oeisdata/seq/A359/A359491.seq
f0c0ba7bc1eea417f6c692f4b35e58ba
A359492
a(n) is the least number of the form p^2 + q^2 - 2 for primes p and q that is an odd prime times 2^n, or -1 if there is no such number.
[ "11", "6", "-1", "56", "48", "96", "192", "384", "2816", "1536", "109568", "10582016", "12288", "7429922816", "64176128", "4318724096", "196608", "60486975488", "9388028592128", "849566088298496", "214058289594368", "896029329195008" ]
[ "sign", "more" ]
17
0
1
[ "A045636", "A359439", "A359492" ]
null
Robert Israel, Jan 02 2023
2023-01-06T10:43:50
oeisdata/seq/A359/A359492.seq
abf73941316dc28b3f10fe371f1769e0
A359493
Numbers k such that the bottom entry in the ratio d(i)/d(i+1) triangle of the elements in the divisors of n, where d(1) < d(2) < ... < d(q) denote the divisors of k, is equal to 1.
[ "1", "4", "8", "9", "16", "25", "27", "32", "36", "49", "64", "81", "100", "121", "125", "128", "144", "169", "196", "225", "243", "256", "289", "324", "343", "361", "400", "441", "484", "512", "529", "576", "625", "676", "729", "784", "841", "900", "961", "1024", "1089", "1156", "1225", "1296", "1331", "1369", "1444", "1521", "1600", "1681", "1764", "1849", "1936" ]
[ "nonn" ]
24
1
2
[ "A001597", "A359247", "A359493" ]
null
Michel Lagneau, Jan 03 2023
2023-02-12T10:38:22
oeisdata/seq/A359/A359493.seq
665a63ad195b52fe6d0e0ef308d9647c
A359494
Zeroless numbers k which can be written as a product of the powers whose base is a digit of k and whose exponent is a nonnegative integer.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "25", "32", "36", "64", "125", "128", "135", "175", "216", "243", "256", "324", "375", "384", "432", "512", "625", "672", "729", "735", "784", "864", "875", "1296", "1372", "1715", "1764", "1792", "2592", "2744", "2916", "3125", "3375", "3456", "3645", "3675", "4375", "5832", "6144", "6272", "6912", "7776", "8192", "8575", "9216" ]
[ "nonn", "base" ]
44
1
2
[ "A002473", "A238985", "A359494" ]
null
Felix Huber, Jan 03 2023
2024-04-28T11:11:03
oeisdata/seq/A359/A359494.seq
6be758d1942b88e3dd3c62429eab4b14
A359495
Sum of positions of 1's in binary expansion minus sum of positions of 1's in reversed binary expansion, where positions in a sequence are read starting with 1 from the left.
[ "0", "0", "-1", "0", "-2", "0", "-2", "0", "-3", "0", "-2", "1", "-4", "-1", "-3", "0", "-4", "0", "-2", "2", "-4", "0", "-2", "2", "-6", "-2", "-4", "0", "-6", "-2", "-4", "0", "-5", "0", "-2", "3", "-4", "1", "-1", "4", "-6", "-1", "-3", "2", "-5", "0", "-2", "3", "-8", "-3", "-5", "0", "-7", "-2", "-4", "1", "-9", "-4", "-6", "-1", "-8", "-3", "-5", "0", "-6", "0", "-2", "4", "-4", "2", "0", "6" ]
[ "sign", "look", "base" ]
21
0
5
[ "A000120", "A029931", "A030190", "A030308", "A048793", "A053632", "A070939", "A222955", "A230877", "A231204", "A291166", "A326669", "A326672", "A326673", "A359042", "A359043", "A359401", "A359402", "A359495" ]
null
Gus Wiseman, Jan 05 2023
2023-01-09T12:41:35
oeisdata/seq/A359/A359495.seq
c37d6e2e27d826a79a17d8e7bd71721a
A359496
Nonnegative integers whose sum of positions of 1's in their binary expansion is less than the sum of positions of 1's in their reversed binary expansion, where positions in a sequence are read starting with 1 from the left.
[ "2", "4", "6", "8", "10", "12", "13", "14", "16", "18", "20", "22", "24", "25", "26", "28", "29", "30", "32", "34", "36", "38", "40", "41", "42", "44", "46", "48", "49", "50", "52", "53", "54", "56", "57", "58", "59", "60", "61", "62", "64", "66", "68", "72", "74", "76", "80", "81", "82", "84", "86", "88", "89", "90", "92", "94", "96", "97", "98", "100", "101", "102", "104", "105", "106" ]
[ "nonn", "base" ]
12
1
1
[ "A000120", "A029931", "A030190", "A030308", "A048793", "A051293", "A053632", "A070939", "A222955", "A230877", "A231204", "A291166", "A304818", "A326669", "A326672", "A326673", "A358194", "A359043", "A359401", "A359402", "A359495", "A359496" ]
null
Gus Wiseman, Jan 18 2023
2023-03-07T19:04:19
oeisdata/seq/A359/A359496.seq
e0bac97539c2382184a75b42c77102d5
A359497
Greatest positive integer whose weakly increasing prime indices have weighted sum (A304818) equal to n.
[ "1", "2", "3", "5", "7", "11", "13", "17", "19", "25", "29", "35", "49", "55", "77", "121", "91", "143", "169", "187", "221", "289", "247", "323", "361", "391", "437", "539", "605", "847", "1331", "715", "1001", "1573", "1183", "1859", "2197", "1547", "2431", "2873", "3179", "3757", "4913", "3553", "4199", "5491", "4693", "6137", "6859", "9317", "14641" ]
[ "nonn" ]
13
0
2
[ "A001222", "A001248", "A029931", "A055932", "A056239", "A089633", "A112798", "A243055", "A304818", "A318283", "A320387", "A358136", "A358137", "A358194", "A359043", "A359361", "A359497", "A359676", "A359678", "A359679", "A359681", "A359682", "A359683", "A359755" ]
null
Gus Wiseman, Jan 15 2023
2023-01-21T22:26:51
oeisdata/seq/A359/A359497.seq
5c00dbd6180f3b5dd87dbd5d4439e96c
A359498
a(n) = ((2*n+1)^8 - 1)/32.
[ "0", "205", "12207", "180150", "1345210", "6698715", "25491585", "80090332", "217992420", "530736345", "1181964355", "2447218290", "4768371582", "8825923015", "15632700405", "26652844920", "43950269320", "70371105957", "109764982935", "167250289390", "249528913410", "365256258675", "525472668457", "744102708180" ]
[ "nonn", "easy" ]
18
0
2
[ "A000217", "A219086", "A359498", "A359499" ]
null
Jianing Song, Jan 03 2023
2025-01-23T12:37:47
oeisdata/seq/A359/A359498.seq
f0749bc313615009d5976004da0a2fcd
A359499
a(n) = ((2*n+1)^16 - 1)/64.
[ "0", "672605", "2384185791", "519264540150", "28953440450810", "717964529118315", "10397134518487185", "102631380558013916", "760331123057294820", "4506897086994080745", "22352635785031020755", "95822037745015603890", "363797880709171295166", "1246350673076132966615", "3910101151255427324805" ]
[ "nonn", "easy" ]
22
0
2
[ "A000217", "A219086", "A359498", "A359499" ]
null
Jianing Song, Jan 03 2023
2024-10-04T10:04:20
oeisdata/seq/A359/A359499.seq
74165b8beb2944e2c87efd3e1892eedf
A359500
a(n) = (7^2^n - 1)/2^(n+3).
[ "3", "75", "90075", "259632270075", "4314170602515315024630075", "2382344702413741601833152075318304337413311121350075", "1452944967966417671787414728262962471027692106596483349510252251060925112718067382475349181570930962790075" ]
[ "nonn", "easy" ]
18
1
1
[ "A068531", "A097421", "A261066", "A359500" ]
null
Jianing Song, Jan 03 2023
2025-02-10T20:49:10
oeisdata/seq/A359/A359500.seq
943960c7684bb9b1e15453f44812da92