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1999-12-11 03:00:00
2025-04-28 00:58:08
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A357801
Coefficients T(n,k) of x^(4*n)*r^(4*k)/(4*n)! in power series C(x,r) = 1 + Integral S(x,r)^3 * D(x,r)^3 dx such that C(x,r)^4 - S(x,r)^4 = 1 and D(x,r)^4 - r^4*S(x,r)^4 = 1, as a triangle read by rows.
[ "1", "6", "0", "2268", "6048", "0", "7434504", "56282688", "35126784", "0", "95227613712", "1409371197696", "2514356038656", "679185948672", "0", "3354162536029536", "81696140755536384", "284770675495950336", "220415417637617664", "33022883487154176", "0", "264444869673131894208", "9583398717725834749440", "54913653475645427527680", "83079959422282198548480", "35701050229143616880640", "3393656235362623684608", "0" ]
[ "nonn", "tabl" ]
22
0
2
[ "A153300", "A357541", "A357800", "A357801", "A357802", "A357805" ]
null
Paul D. Hanna, Oct 14 2022
2023-04-12T22:45:02
oeisdata/seq/A357/A357801.seq
305bda949d267f61c72a6f0193dcfbcd
A357802
Coefficients T(n,k) of x^(4*n)*r^(4*k)/(4*n)! in power series D(x,r) = 1 + r^4 * Integral S(x,r)^3 * C(x,r)^3 dx such that C(x,r)^4 - S(x,r)^4 = 1 and D(x,r)^4 - r^4*S(x,r)^4 = 1, as a triangle read by rows.
[ "1", "0", "6", "0", "6048", "2268", "0", "35126784", "56282688", "7434504", "0", "679185948672", "2514356038656", "1409371197696", "95227613712", "0", "33022883487154176", "220415417637617664", "284770675495950336", "81696140755536384", "3354162536029536", "0", "3393656235362623684608", "35701050229143616880640", "83079959422282198548480", "54913653475645427527680", "9583398717725834749440", "264444869673131894208" ]
[ "nonn", "tabl" ]
10
0
3
[ "A153300", "A357542", "A357800", "A357801", "A357802", "A357805" ]
null
Paul D. Hanna, Oct 14 2022
2023-04-12T22:49:15
oeisdata/seq/A357/A357802.seq
a44c8fa4ed2e8ed56eb482036fddb5c1
A357803
a(n) = coefficient of x^(2*n) in A(x) such that A(x) = G(x)^2 where G(x) = 1 + Sum_{n>=1} (-1)^n * x^(4*n^2) * (F(x/2)^(2*n) + F(-x/2)^(2*n)), and F(x) is the g.f. of A357787.
[ "1", "0", "-4", "-8", "-12", "-8", "32", "128", "292", "440", "248", "-904", "-3616", "-7032", "-5824", "13056", "66372", "146144", "145116", "-250216", "-1545848", "-3862464", "-5072992", "2525376", "33963072", "100587096", "164044888", "37400880", "-712627392", "-2586929240", "-5043112640", "-3653527040", "13772747140", "65564551200", "150393547384", "167883535904" ]
[ "sign" ]
6
0
3
[ "A357787", "A357788", "A357789", "A357803", "A357806" ]
null
Paul D. Hanna, Dec 06 2022
2022-12-08T07:35:55
oeisdata/seq/A357/A357803.seq
df402096318eda344e501ce3e8dd65bc
A357804
a(n) = coefficient of x^(4*n+1)/(4*n+1)! in power series S(x) = Series_Reversion( Integral 1/(1 + x^4)^(3/2) dx ).
[ "1", "36", "87696", "1483707456", "91329084354816", "14862901723860427776", "5279211177231308343054336", "3600188413031639396548043882496", "4300014195136238449156877005063520256", "8394333803654997846112872487491938363375616", "25378508500092778024069322428694679252236239896576" ]
[ "nonn" ]
17
0
2
[ "A153301", "A357800", "A357804", "A357805" ]
null
Paul D. Hanna, Oct 14 2022
2025-04-09T06:34:42
oeisdata/seq/A357/A357804.seq
6307cd51c927fde17e11d9c78fb32502
A357805
a(n) = coefficient of x^(4*n)/(4*n)! in power series C(x) = 1 + Integral S(x)^3 * C(x)^3 dx such that C(x)^4 - S(x)^4 = 1.
[ "1", "6", "8316", "98843976", "4698140798736", "623259279912288096", "186936162949832833285056", "110352751044119383032310847616", "116215132158682166284921510741483776", "202905498509713715271588290261091671041536", "554890365215965228675768455367962915432839248896" ]
[ "nonn" ]
12
0
2
[ "A153300", "A357801", "A357802", "A357804", "A357805" ]
null
Paul D. Hanna, Oct 14 2022
2022-12-03T12:01:59
oeisdata/seq/A357/A357805.seq
e4affb4c0073ff29a0ecaf128ae9c2d2
A357806
a(n) = coefficient of x^(2*n) in A(x) = 1 + Sum_{n>=1} (-1)^n * x^(4*n^2) * (F(x/2)^(2*n) + F(-x/2)^(2*n)), where F(x) is the g.f. of A357787.
[ "1", "0", "-2", "-4", "-8", "-12", "-8", "8", "50", "108", "120", "-68", "-672", "-1644", "-1904", "1912", "15456", "41160", "59494", "-5852", "-311040", "-996744", "-1752680", "-840600", "5988928", "24181500", "50438488", "45910304", "-103373216", "-582387300", "-1428882832", "-1814475760", "1263429058", "13685575400" ]
[ "sign" ]
10
0
3
[ "A357787", "A357788", "A357789", "A357806" ]
null
Paul D. Hanna, Dec 05 2022
2022-12-06T10:23:06
oeisdata/seq/A357/A357806.seq
4b2b476a47d0d7822441ec4aa4ff5e97
A357807
Semiprimes k such that k is congruent to 3 modulo k's index in the sequence of semiprimes.
[ "4", "9", "15", "111", "141", "237", "27663", "27667", "3066878", "3066893", "3067023", "3067033", "3067073", "3067193", "3067243", "3067273", "3067283", "3067543", "3067598", "3067613", "3067663", "3067798", "3067843", "3067853", "3067913", "3067933", "3067993", "348933171", "348933219", "348933297" ]
[ "nonn", "hard" ]
10
1
1
[ "A001358", "A106128", "A357807" ]
null
Lucas A. Brown, Oct 13 2022
2022-10-16T03:23:53
oeisdata/seq/A357/A357807.seq
43ae4aa45b9b1ebdb839bae28acfb9ae
A357808
Semiprimes k such that k is congruent to 4 modulo k's index in the sequence of semiprimes.
[ "4", "6", "14", "115", "118", "178", "187", "214", "235", "3066899", "3067069", "3067079", "3067149", "3067429", "3067549", "3067594", "3067609", "3067669", "3067719", "3067999", "44690978147", "44690978217", "44690978245", "44690978623", "44690978903", "44690979022", "44690979442" ]
[ "nonn", "hard", "more" ]
10
1
1
[ "A001358", "A106129", "A357808" ]
null
Lucas A. Brown, Oct 13 2022
2022-10-29T04:42:40
oeisdata/seq/A357/A357808.seq
7b235e7d3a94b8aa0a991147cff1653c
A357809
Locations of successive records in A357062.
[ "0", "4", "6", "12", "24", "36", "40", "54", "60", "84", "96", "120", "144", "168", "180", "264", "360", "420", "504", "600", "840", "1176", "1320", "1440", "1680", "2280", "2520", "3024", "3120", "3960", "6120", "6300", "7560", "7800", "8160", "11760", "14040", "19320", "21600", "27720", "30240", "38760", "52920", "55440", "65520", "83160", "85680" ]
[ "nonn", "hard" ]
12
1
2
[ "A357062", "A357809" ]
null
Charles R Greathouse IV, Oct 13 2022
2022-10-21T11:39:03
oeisdata/seq/A357/A357809.seq
aca2642387ad86c2111daf328daab151
A357810
Number of n-step closed paths on the Cairo pentagonal lattice graph starting from a degree-4 node.
[ "1", "0", "4", "0", "24", "8", "164", "136", "1236", "1704", "10116", "19144", "88616", "205208", "818764", "2155160", "7873440", "22463400", "77954740", "233894600", "788314984", "2440865400", "8095906076", "25569342520", "84107990356", "269034666280" ]
[ "nonn", "easy", "walk" ]
12
0
3
[ "A002893", "A002894", "A002898", "A357810", "A357811" ]
null
Dave R.M. Langers, Oct 13 2022
2022-11-27T11:32:16
oeisdata/seq/A357/A357810.seq
bd977ab5dd350d4f4fa5a6915862dcc9
A357811
Number of n-step closed paths on the Cairo pentagonal lattice graph starting from a degree-3 node.
[ "1", "0", "3", "0", "17", "6", "115", "100", "867", "1236", "7117", "13770", "62545", "146866", "579387", "1537920", "5581725", "16002810", "55329435", "166465820", "559913787", "1736268432", "5752600961", "18182999274", "59777071435", "191287075320" ]
[ "nonn", "easy", "walk" ]
11
0
3
[ "A002893", "A002894", "A002898", "A357810", "A357811" ]
null
Dave R.M. Langers, Oct 13 2022
2022-11-27T11:32:27
oeisdata/seq/A357/A357811.seq
cc290c80c4f476d314f538338497efd6
A357812
Number of subsets of [n] in which exactly half of the elements are powers of 2.
[ "1", "1", "1", "3", "4", "10", "20", "35", "70", "126", "210", "330", "495", "715", "1001", "1365", "4368", "6188", "8568", "11628", "15504", "20349", "26334", "33649", "42504", "53130", "65780", "80730", "98280", "118755", "142506", "169911", "906192", "1107568", "1344904", "1623160", "1947792", "2324784", "2760681", "3262623", "3838380" ]
[ "nonn" ]
22
0
4
[ "A000079", "A029837", "A037031", "A102366", "A113473", "A180272", "A357812", "A357927" ]
null
Alois P. Heinz, Oct 13 2022
2022-10-20T17:35:33
oeisdata/seq/A357/A357812.seq
6123834215b0917a0d2c9bfd20c3d429
A357813
a(n) is the least number k such that the sum of n^2 consecutive primes starting at prime(k) is a square.
[ "3", "1", "78", "333", "84", "499", "36", "1874", "1102", "18", "183", "2706", "23", "104", "739", "1055", "8435", "633", "42130", "13800", "942", "55693", "7449", "13270", "41410", "4317", "17167", "61999", "17117", "9161", "46704", "12447", "2679", "2971", "3946", "103089", "6359", "19601", "7240", "422", "690", "20851", "963", "36597", "3559", "111687", "12926", "4071", "30622", "6355" ]
[ "nonn" ]
55
2
1
[ "A034963", "A127336", "A230327", "A357813", "A358156" ]
null
Jean-Marc Rebert, Nov 12 2022
2022-12-15T21:24:23
oeisdata/seq/A357/A357813.seq
ba8385eb9b5afb9c398e4fc23392c7d6
A357814
Triangular array read by rows: T(n,k) is the quotient on division of Fib(n) by Fib(k) for 1 <= k <= n, where Fib(k) = A000045(k).
[ "1", "1", "1", "2", "2", "1", "3", "3", "1", "1", "5", "5", "2", "1", "1", "8", "8", "4", "2", "1", "1", "13", "13", "6", "4", "2", "1", "1", "21", "21", "10", "7", "4", "2", "1", "1", "34", "34", "17", "11", "6", "4", "2", "1", "1", "55", "55", "27", "18", "11", "6", "4", "2", "1", "1", "89", "89", "44", "29", "17", "11", "6", "4", "2", "1", "1", "144", "144", "72", "48", "28", "18", "11", "6", "4", "2", "1", "1", "233", "233", "116", "77", "46", "29", "17", "11" ]
[ "nonn", "tabl", "look" ]
33
1
4
[ "A000032", "A000045", "A357724", "A357814" ]
null
J. M. Bergot and Robert Israel, Oct 13 2022
2022-10-25T20:04:07
oeisdata/seq/A357/A357814.seq
6b3e5dfb58cdc1fe5c784ed5d88a2e38
A357815
Smallest maximum degree over all maximal 2-degenerate graphs with diameter 2 and n vertices.
[ "0", "1", "2", "3", "3", "4", "4", "4", "4", "5", "6", "6", "7", "8", "9", "10", "11", "12", "12", "13", "14", "14", "15", "16", "16", "17", "18", "18", "19", "20", "20", "21", "22", "22", "23", "24", "24", "25", "26", "26", "27", "28", "28", "29", "30", "30", "31", "32", "32", "33", "34", "34", "35", "36", "36", "37", "38", "38", "39", "40" ]
[ "nonn" ]
7
1
3
[ "A004523", "A357815" ]
null
Allan Bickle, Oct 13 2022
2022-11-27T11:20:19
oeisdata/seq/A357/A357815.seq
8a268440b381cf2c930435b696242f37
A357816
a(n) is the first even number k such that there are exactly n pairs (p,q) where p and q are prime, p<=q, p+q = k, and p+A001414(k) and q+A001414(k) are also prime.
[ "2", "16", "60", "72", "220", "132", "374", "276", "492", "638", "636", "852", "620", "854", "996", "1056", "1026", "1212", "2070", "1530", "2610", "3976", "3844", "1488", "1572", "4812", "4770", "3942", "2484", "5028", "3234", "4668", "6036", "3276", "5172", "5532", "6756", "2730", "6084", "4230", "6390", "9132", "14134", "4620", "9674", "10692", "6600", "8910", "10836", "12204", "18852", "9660" ]
[ "nonn" ]
9
0
1
[ "A001414", "A023036", "A357816" ]
null
J. M. Bergot and Robert Israel, Oct 13 2022
2022-10-24T10:58:04
oeisdata/seq/A357/A357816.seq
614dde1b3b560ff578036181400b2c00
A357817
Partial alternating sums of the Dedekind psi function (A001615): a(n) = Sum_{k=1..n} (-1)^(k+1) * psi(k).
[ "1", "-2", "2", "-4", "2", "-10", "-2", "-14", "-2", "-20", "-8", "-32", "-18", "-42", "-18", "-42", "-24", "-60", "-40", "-76", "-44", "-80", "-56", "-104", "-74", "-116", "-80", "-128", "-98", "-170", "-138", "-186", "-138", "-192", "-144", "-216", "-178", "-238", "-182", "-254", "-212", "-308", "-264", "-336", "-264", "-336", "-288", "-384", "-328", "-418" ]
[ "sign" ]
15
1
2
[ "A001615", "A068762", "A068773", "A173290", "A307704", "A357817" ]
null
Amiram Eldar, Oct 14 2022
2024-02-29T13:30:30
oeisdata/seq/A357/A357817.seq
0350a045b3b220d7d78522c009433bd8
A357818
Numerators of the partial sums of the reciprocals of the Dedekind psi function (A001615).
[ "1", "4", "19", "7", "23", "2", "17", "53", "55", "169", "175", "89", "641", "1303", "331", "1345", "1373", "1387", "7061", "2377", "9613", "29119", "29539", "29749", "6017", "6065", "6121", "6163", "31151", "31291", "15803", "3977", "16013", "48319", "24317", "12211", "233899", "58774", "472757", "59344", "119543", "1918673", "21249043", "21336823" ]
[ "nonn", "frac" ]
11
1
2
[ "A001615", "A001620", "A028415", "A065463", "A104528", "A173290", "A212717", "A335707", "A357818", "A357819" ]
null
Amiram Eldar, Oct 14 2022
2022-10-15T07:17:25
oeisdata/seq/A357/A357818.seq
ae8df31558edde105e27994760220860
A357819
Denominators of the partial sums of the reciprocals of the Dedekind psi function (A001615).
[ "1", "3", "12", "4", "12", "1", "8", "24", "24", "72", "72", "36", "252", "504", "126", "504", "504", "504", "2520", "840", "3360", "10080", "10080", "10080", "2016", "2016", "2016", "2016", "10080", "10080", "5040", "1260", "5040", "15120", "7560", "3780", "71820", "17955", "143640", "17955", "35910", "574560", "6320160", "6320160", "6320160", "6320160" ]
[ "nonn", "frac" ]
9
1
2
[ "A001615", "A048049", "A104529", "A173290", "A212718", "A357818", "A357819" ]
null
Amiram Eldar, Oct 14 2022
2022-10-15T07:19:28
oeisdata/seq/A357/A357819.seq
04c55594781ae1fcfb5bd902eb04a35e
A357820
Numerators of the partial alternating sums of the reciprocals of the Dedekind psi function (A001615).
[ "1", "2", "11", "3", "11", "5", "23", "7", "23", "65", "71", "17", "64", "491", "64", "491", "173", "505", "2651", "2581", "10639", "1151", "3593", "3523", "727", "237", "2189", "2147", "11071", "10931", "5623", "2759", "5623", "16589", "2113", "8347", "162373", "159979", "20318", "160549", "163969", "649891", "7292441", "7204661", "7292441", "7204661" ]
[ "nonn", "frac" ]
9
1
2
[ "A001615", "A001620", "A065463", "A173290", "A211177", "A335707", "A357820", "A357821" ]
null
Amiram Eldar, Oct 14 2022
2022-10-15T07:21:24
oeisdata/seq/A357/A357820.seq
229ab0a49c1895a2b17481f80261b7a1
A357821
Denominators of the partial alternating sums of the reciprocals of the Dedekind psi function (A001615).
[ "1", "3", "12", "4", "12", "6", "24", "8", "24", "72", "72", "18", "63", "504", "63", "504", "168", "504", "2520", "2520", "10080", "1120", "3360", "3360", "672", "224", "2016", "2016", "10080", "10080", "5040", "2520", "5040", "15120", "1890", "7560", "143640", "143640", "17955", "143640", "143640", "574560", "6320160", "6320160", "6320160", "6320160" ]
[ "nonn", "frac" ]
8
1
2
[ "A001615", "A173290", "A211178", "A357820", "A357821" ]
null
Amiram Eldar, Oct 14 2022
2022-10-15T07:21:58
oeisdata/seq/A357/A357821.seq
341f9aac11ca19e59bc71205d990a175
A357822
Number of simplicial 3-spheres (triangulations of S^3) with n vertices.
[ "1", "2", "5", "39", "1296", "247882", "166564303" ]
[ "nonn", "hard", "more" ]
8
5
2
[ "A000109", "A357822" ]
null
R. J. Mathar, Oct 14 2022
2022-11-24T18:28:10
oeisdata/seq/A357/A357822.seq
a9660a778f5639013597a5fcfc81c0f1
A357823
a(n) is the number of bases > 1 where n is not divisible by the sum of its digits.
[ "0", "0", "1", "0", "3", "0", "5", "1", "4", "3", "9", "1", "11", "9", "7", "5", "15", "5", "17", "7", "11", "17", "21", "5", "18", "20", "17", "14", "27", "12", "29", "16", "24", "28", "24", "13", "35", "33", "31", "17", "39", "22", "41", "33", "26", "41", "45", "18", "42", "34", "42", "38", "51", "33", "45", "35", "48", "53", "57", "26", "59", "57", "44", "41", "52", "43", "65", "56", "60", "48" ]
[ "nonn", "base" ]
38
1
5
[ "A080221", "A138530", "A356555", "A357823" ]
null
Rémy Sigrist, Oct 17 2022
2022-10-21T07:00:01
oeisdata/seq/A357/A357823.seq
e5d84cff9aefe266acabc5118e0c08dd
A357824
Total number A(n,k) of k-tuples of semi-Dyck paths from (0,0) to (n,n-2*j) for j=0..floor(n/2); square array A(n,k), n>=0, k>=0, read by antidiagonals.
[ "1", "1", "1", "1", "1", "2", "1", "1", "2", "2", "1", "1", "2", "3", "3", "1", "1", "2", "5", "6", "3", "1", "1", "2", "9", "14", "10", "4", "1", "1", "2", "17", "36", "42", "20", "4", "1", "1", "2", "33", "98", "190", "132", "35", "5", "1", "1", "2", "65", "276", "882", "980", "429", "70", "5", "1", "1", "2", "129", "794", "4150", "7812", "5705", "1430", "126", "6", "1", "1", "2", "257", "2316", "19722", "65300", "78129", "33040", "4862", "252", "6" ]
[ "nonn", "tabl" ]
29
0
6
[ "A000012", "A000051", "A000108", "A001405", "A001550", "A003161", "A007395", "A008315", "A008619", "A074511", "A120730", "A129123", "A357824", "A357825", "A361887", "A361890", "A382433" ]
null
Alois P. Heinz, Oct 14 2022
2025-03-25T12:02:47
oeisdata/seq/A357/A357824.seq
38f1a4396e5911557f94d689c97240eb
A357825
Total number of n-tuples of semi-Dyck paths from (0,0) to (n,n-2*j) for j = 0..floor(n/2).
[ "1", "1", "2", "9", "98", "4150", "562692", "211106945", "404883552194", "1766902576146876", "40519034229909243476", "2708397617879598970178238", "658332084097982587522119612196", "735037057881394837614680080889845116", "2030001034486747324990010196845670569155080" ]
[ "nonn", "easy" ]
36
0
3
[ "A000108", "A000225", "A008315", "A120730", "A357824", "A357825", "A357871" ]
null
Alois P. Heinz, Oct 14 2022
2023-03-23T03:33:33
oeisdata/seq/A357/A357825.seq
9cea157afdfac746df741a58db06eead
A357826
Base-10 weaker Skolem-Langford numbers.
[ "231213", "312132", "12132003", "23121300", "23421314", "30023121", "31213200", "41312432", "1214230043", "1312432004", "2342131400", "2412134003", "3004312142", "3400324121", "4002342131", "4131243200", "4562342536", "4635243265", "5364235246", "5623425364", "6352432654", "6425324635", "14156742352637", "14167345236275" ]
[ "nonn", "base", "easy", "fini", "full" ]
46
1
1
[ "A108116", "A132291", "A339803", "A357826" ]
null
Marc Morgenegg, Oct 14 2022
2022-12-11T13:51:41
oeisdata/seq/A357/A357826.seq
950a11ec752c002ae7ad2389ecdbd096
A357827
Number of automorphisms of the n-folded cube graph.
[ "2", "24", "1152", "1920", "23040", "322560", "5160960", "92897280", "1857945600", "40874803200", "980995276800", "25505877196800", "714164561510400", "21424936845312000", "685597979049984000" ]
[ "nonn", "more" ]
5
2
1
[ "A000165", "A288944", "A357827" ]
null
Pontus von Brömssen, Oct 14 2022
2022-10-14T12:48:32
oeisdata/seq/A357/A357827.seq
53ceae6e7cdcd31afae2c6519a60d61c
A357828
a(n) = Sum_{k=0..floor(n/3)} |Stirling1(n,3*k)|.
[ "1", "0", "0", "1", "6", "35", "226", "1645", "13454", "122661", "1236018", "13656951", "164290182", "2138379243", "29949509226", "449188719525", "7183702249542", "122039922034485", "2194928052851898", "41666342509646127", "832547791827455886", "17466905709043534107", "383908421683657311714" ]
[ "nonn" ]
17
0
5
[ "A003703", "A357828", "A357829", "A357830" ]
null
Seiichi Manyama, Oct 14 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357828.seq
b8dbba23c1e09688e183143c8ada30eb
A357829
a(n) = Sum_{k=0..floor((n-1)/3)} |Stirling1(n,3*k+1)|.
[ "0", "1", "1", "2", "7", "34", "205", "1456", "11837", "108150", "1096011", "12196128", "147814359", "1938062490", "27333191613", "412614191808", "6638401596645", "113398127795862", "2049808094564139", "39091473755006400", "784404343854767727", "16520634668922810426", "364400233756422553053" ]
[ "nonn" ]
13
0
4
[ "A357828", "A357829", "A357830" ]
null
Seiichi Manyama, Oct 14 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357829.seq
79523d8b4d1bc3f458325a8fc17b3d29
A357830
a(n) = Sum_{k=0..floor((n-2)/3)} |Stirling1(n,3*k+2)|.
[ "0", "0", "1", "3", "11", "51", "289", "1939", "15029", "132069", "1296771", "14063721", "166897059", "2150579067", "29895590361", "445871456667", "7100686041813", "120249378265653", "2157637558311963", "40887284144179473", "815949872494416387", "17103401793743095467", "375692072337527815233" ]
[ "nonn" ]
19
0
4
[ "A357828", "A357829", "A357830" ]
null
Seiichi Manyama, Oct 14 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357830.seq
0dd82ade1def3af7ac3674cf66683fa0
A357831
a(n) = Sum_{k=0..floor(n/3)} 2^k * |Stirling1(n,3*k)|.
[ "1", "0", "0", "2", "12", "70", "454", "3332", "27552", "254400", "2598852", "29125932", "355455468", "4693396656", "66671326176", "1013916648840", "16436063079552", "282920894841096", "5153797995148296", "99052313167391760", "2003040751641857856", "42513854724369719136", "944959706480298199824" ]
[ "nonn" ]
15
0
4
[ "A357831", "A357832", "A357833" ]
null
Seiichi Manyama, Oct 14 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357831.seq
9f608cbae4f063d36c53426a18f0c758
A357832
a(n) = Sum_{k=0..floor((n-1)/3)} 2^k * |Stirling1(n,3*k+1)|.
[ "0", "1", "1", "2", "8", "44", "290", "2194", "18690", "177072", "1848048", "21079332", "260998584", "3487438476", "50030096844", "767092681992", "12520306878720", "216760973139072", "3967857438205320", "76575231882844056", "1553981718941428824", "33082675130470434336", "737250032464248840192" ]
[ "nonn" ]
21
0
4
[ "A357831", "A357832", "A357833" ]
null
Seiichi Manyama, Oct 14 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357832.seq
f6ab2f0b9456288443301cb0ce4692fb
A357833
a(n) = Sum_{k=0..floor((n-2)/3)} 2^k * |Stirling1(n,3*k+2)|.
[ "0", "0", "1", "3", "11", "52", "304", "2114", "16992", "154626", "1568706", "17535108", "213965520", "2828584824", "40259041188", "613656673476", "9971942784132", "172071391424832", "3141974627361216", "60523400730707208", "1226519845766281008", "26084378634267048984", "580854626450078463000" ]
[ "nonn" ]
15
0
4
[ "A357831", "A357832", "A357833" ]
null
Seiichi Manyama, Oct 14 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357833.seq
caadcb6df50ad49ad4441fceaee3a08c
A357834
a(n) = Sum_{k=0..floor(n/3)} Stirling1(n,3*k).
[ "1", "0", "0", "1", "-6", "35", "-224", "1603", "-12810", "113589", "-1109472", "11852841", "-137611110", "1726238787", "-23277264192", "335861699355", "-5164348236138", "84316474011861", "-1456893047937600", "26562992204112273", "-509679388313669574", "10266675502780006947", "-216625348636705401120" ]
[ "sign" ]
14
0
5
[ "A105752", "A357834", "A357835", "A357836" ]
null
Seiichi Manyama, Oct 14 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357834.seq
6bcca63c2130b80472959c5d49fdfcb2
A357835
a(n) = Sum_{k=0..floor((n-1)/3)} Stirling1(n,3*k+1).
[ "0", "1", "-1", "2", "-5", "14", "-35", "-14", "1701", "-26418", "351351", "-4622982", "62705643", "-890078826", "13297263525", "-209438953542", "3477446002485", "-60803484275898", "1117975706702127", "-21580455768575886", "436591651807054107", "-9241512424454751714", "204338436416329792941" ]
[ "sign" ]
14
0
4
[ "A357834", "A357835", "A357836" ]
null
Seiichi Manyama, Oct 14 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357835.seq
8056147a3c817c45256f9ec2eeccefc5
A357836
a(n) = Sum_{k=0..floor((n-2)/3)} Stirling1(n,3*k+2).
[ "0", "0", "1", "-3", "11", "-49", "259", "-1589", "11109", "-87171", "758121", "-7229859", "74905467", "-836159961", "9980000667", "-126422745813", "1686902233653", "-23512989735963", "338917341235473", "-4982536435536387", "73087736506615467", "-1025163078325255233", "12286912220375608179" ]
[ "sign" ]
13
0
4
[ "A357834", "A357835", "A357836" ]
null
Seiichi Manyama, Oct 14 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357836.seq
7ae45391ab25cdc070dfdbc560278078
A357837
a(n) is the sum of the lengths of all the segments used to draw a square of side n representing a fishbone pattern using symmetric L-shaped tiles with side length 2.
[ "0", "4", "10", "20", "32", "46", "64", "84", "106", "132", "160", "190", "224", "260", "298", "340", "384", "430", "480", "532", "586", "644", "704", "766", "832", "900", "970", "1044", "1120", "1198", "1280", "1364", "1450", "1540", "1632", "1726", "1824", "1924", "2026", "2132", "2240", "2350", "2464", "2580", "2698", "2820", "2944", "3070", "3200", "3332" ]
[ "nonn", "easy" ]
43
0
2
[ "A002264", "A002522", "A005843", "A047410", "A071619", "A211547", "A345118", "A357837" ]
null
Stefano Spezia, Oct 17 2022
2023-01-25T09:20:56
oeisdata/seq/A357/A357837.seq
7471ccd97eca603c4a3b9708cb6a3672
A357838
Decimal expansion of Wien frequency displacement law constant.
[ "5", "8", "7", "8", "9", "2", "5", "7", "5", "7", "6", "4", "6", "8", "2", "4", "9", "4", "6", "6", "0", "6", "1", "3", "0", "7", "9", "5", "3", "0", "9", "7", "2", "1", "6", "9", "1", "4", "7", "5", "1", "4", "4", "2", "5", "8", "8", "8", "2", "9", "2", "3", "0", "8", "2", "8", "3", "5", "2", "9", "6", "0", "3", "9", "3", "6", "0", "8", "9", "2", "6", "5", "2", "6", "4", "0", "0", "2", "3", "8", "6", "1", "9", "6", "5", "8", "5" ]
[ "nonn", "cons" ]
14
11
1
[ "A003676", "A070063", "A081819", "A194567", "A357838" ]
null
Lee A. Newberg, Oct 14 2022
2022-10-24T00:01:34
oeisdata/seq/A357/A357838.seq
ef1964cc4067366d5c64458dea16b9ce
A357839
a(n) is the greatest divisor > 1 of n which has already been listed, otherwise a(n) is the smallest number not yet listed; a(1) = 0.
[ "0", "1", "2", "2", "3", "3", "4", "4", "3", "2", "5", "4", "6", "2", "5", "4", "7", "6", "8", "5", "7", "2", "9", "8", "5", "2", "9", "7", "10", "10", "11", "8", "11", "2", "7", "9", "12", "2", "3", "10", "13", "7", "14", "11", "9", "2", "15", "12", "7", "10", "3", "13", "16", "9", "11", "14", "3", "2", "17", "15", "18", "2", "9", "16", "13", "11", "19", "17", "3", "14", "20", "18", "21", "2", "15", "19", "11" ]
[ "nonn", "easy" ]
12
1
3
[ "A008336", "A008344", "A051352", "A357839" ]
null
Samuel Harkness, Oct 14 2022
2022-11-27T12:13:06
oeisdata/seq/A357/A357839.seq
4a46374f5c6c8164d924bdca1beb4d74
A357840
Numbers k in A018900 with arithmetic derivative k' (A003415) in A018900.
[ "6", "9", "20", "40", "65", "68", "96", "144", "192", "528", "576", "1028", "4097", "73728", "81920", "262148", "557056", "6291456", "9437184", "12582912", "201326592", "335544320", "2415919104", "1374389534720", "11258999068426240", "90071992547409920", "648518346341351424", "78398662313265594368", "116056878683004400771792896" ]
[ "nonn", "base" ]
18
1
1
[ "A003415", "A018900", "A019434", "A357840" ]
null
Marius A. Burtea, Oct 20 2022
2022-11-19T21:50:29
oeisdata/seq/A357/A357840.seq
62cfbbf60008ab8384ef8e4684bdde99
A357841
Smith numbers (A006753) for which the arithmetic derivative (A003415) is also a Smith number.
[ "4", "27", "85", "121", "166", "265", "517", "526", "634", "706", "778", "913", "985", "1633", "1822", "1966", "2173", "2218", "2326", "2434", "2605", "2785", "3505", "3802", "3865", "3973", "4306", "4369", "4765", "4918", "5248", "5674", "5818", "5926", "6178", "6385", "7186", "7726", "8185", "8257", "8653", "9193", "9301", "10201", "10489", "10606" ]
[ "nonn", "base" ]
10
1
1
[ "A003415", "A006753", "A357841" ]
null
Marius A. Burtea, Oct 20 2022
2022-11-19T21:50:41
oeisdata/seq/A357/A357841.seq
ed25d01702d5f312722dae24205fa3ba
A357842
a(n) is the smallest number k for which k and the arithmetic derivative k' (A003415) have exactly n triangular divisors (A000217).
[ "2", "27", "18", "72", "612", "1764", "756", "8100", "27000", "97200", "66528", "175500", "93600", "280800", "1731600", "661500", "680400", "3704400", "34177500", "11107800", "16581600", "20065500", "108486000", "102910500", "108353700", "181912500", "314874000", "462672000", "4408236000", "229975200", "2297786400", "672348600", "925041600", "1344697200", "158230800" ]
[ "nonn" ]
23
1
1
[ "A000217", "A003415", "A007862", "A130317", "A357842" ]
null
Marius A. Burtea, Oct 20 2022
2022-11-19T21:51:14
oeisdata/seq/A357/A357842.seq
ec6e8a9288370b5041b89dd0aa248f15
A357843
Numerators of the partial alternating sums of the reciprocals of the number of divisors function (A000005).
[ "1", "1", "1", "2", "7", "11", "17", "7", "3", "5", "7", "19", "25", "11", "25", "113", "143", "133", "163", "51", "14", "51", "61", "117", "391", "361", "391", "371", "431", "52", "119", "19", "81", "19", "81", "709", "799", "377", "799", "1553", "1733", "211", "467", "226", "467", "889", "979", "961", "1021", "991", "259", "503", "274", "2147", "2237", "274", "1141", "274" ]
[ "nonn", "frac" ]
14
1
4
[ "A000005", "A104528", "A211177", "A307704", "A357820", "A357843", "A357844" ]
null
Amiram Eldar, Oct 16 2022
2022-10-17T01:43:18
oeisdata/seq/A357/A357843.seq
35edf0dd7546a903acedc22629894d69
A357844
Denominators of the partial alternating sums of the reciprocals of the number of divisors function (A000005).
[ "1", "2", "1", "3", "6", "12", "12", "6", "2", "4", "4", "12", "12", "6", "12", "60", "60", "60", "60", "20", "5", "20", "20", "40", "120", "120", "120", "120", "120", "15", "30", "5", "20", "5", "20", "180", "180", "90", "180", "360", "360", "45", "90", "45", "90", "180", "180", "180", "180", "180", "45", "90", "45", "360", "360", "45", "180", "45", "90", "180", "180", "45", "90", "630" ]
[ "nonn", "frac" ]
9
1
2
[ "A000005", "A104529", "A211178", "A307704", "A357821", "A357843", "A357844" ]
null
Amiram Eldar, Oct 16 2022
2022-10-17T01:43:23
oeisdata/seq/A357/A357844.seq
e6fac376e7c207211268276e82f3dd24
A357845
Numerators of the partial alternating sums of the reciprocals of the sum of divisors function (A000203).
[ "1", "2", "11", "65", "79", "6", "55", "769", "10837", "30691", "33421", "32251", "34591", "16613", "34591", "1039561", "365327", "356647", "373573", "365513", "1504367", "4400261", "4569521", "4501817", "149447", "146327", "149603", "147263", "151631", "49937", "25651", "75913", "38639", "114097", "232289", "230129", "4470731", "4408487" ]
[ "nonn", "frac" ]
13
1
2
[ "A000203", "A065442", "A065443", "A068762", "A104528", "A212717", "A357820", "A357845", "A357846" ]
null
Amiram Eldar, Oct 16 2022
2022-10-17T01:43:26
oeisdata/seq/A357/A357845.seq
1d52a6d7600bee97bf892d9e30f24f56
A357846
Denominators of the partial alternating sums of the reciprocals of the sum of divisors function (A000203).
[ "1", "3", "12", "84", "84", "7", "56", "840", "10920", "32760", "32760", "32760", "32760", "16380", "32760", "1015560", "338520", "338520", "338520", "338520", "1354080", "4062240", "4062240", "4062240", "131040", "131040", "131040", "131040", "131040", "43680", "21840", "65520", "32760", "98280", "196560", "196560", "3734640", "3734640" ]
[ "nonn", "frac" ]
10
1
2
[ "A000203", "A068762", "A104529", "A212718", "A357821", "A357845", "A357846" ]
null
Amiram Eldar, Oct 16 2022
2022-10-17T01:43:30
oeisdata/seq/A357/A357846.seq
c03035ee645abf9cd61e96bc60858eac
A357847
Number of integer compositions of n whose length is twice their alternating sum.
[ "1", "0", "0", "1", "0", "1", "3", "1", "8", "11", "15", "46", "59", "127", "259", "407", "888", "1591", "2925", "5896", "10607", "20582", "39446", "73448", "142691", "269777", "513721", "988638", "1876107", "3600313", "6893509", "13165219", "25288200", "48408011", "92824505", "178248758", "341801149", "656641084", "1261298356" ]
[ "nonn" ]
10
0
7
[ "A011782", "A025047", "A097805", "A103919", "A262977", "A301987", "A344651", "A357136", "A357182", "A357183", "A357184", "A357189", "A357485", "A357486", "A357488", "A357709", "A357847", "A357848" ]
null
Gus Wiseman, Oct 16 2022
2022-10-19T19:50:05
oeisdata/seq/A357/A357847.seq
24788b19df072fa5368007f8dfd5bbc9
A357848
Heinz numbers of integer partitions whose length is twice their alternating sum.
[ "1", "6", "15", "35", "40", "77", "84", "90", "143", "189", "210", "220", "221", "224", "250", "323", "364", "437", "462", "490", "495", "504", "525", "528", "667", "748", "819", "858", "899", "988", "1029", "1040", "1134", "1147", "1155", "1188", "1210", "1320", "1326", "1375", "1400", "1408", "1517", "1564", "1683", "1690", "1763", "1904", "1938", "2021" ]
[ "nonn" ]
5
1
2
[ "A000009", "A000041", "A000720", "A001221", "A001222", "A003963", "A025047", "A056239", "A097805", "A103919", "A262977", "A301987", "A344651", "A357136", "A357182", "A357183", "A357184", "A357189", "A357485", "A357486", "A357488", "A357709", "A357847", "A357848" ]
null
Gus Wiseman, Oct 16 2022
2022-10-17T07:06:57
oeisdata/seq/A357/A357848.seq
a047074c1bf8c61e0e41ccf59ae7c487
A357849
Number of integer partitions (w,x,y) summing to n such that 2w = 3x + 4y.
[ "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "1", "0", "0", "1", "0", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "3", "2", "2", "3", "2", "3", "2", "2", "3", "2", "3", "3", "2", "3", "3", "3", "3", "2", "3", "3", "3", "3", "3", "3" ]
[ "nonn" ]
8
0
34
[ "A000009", "A000041", "A008676", "A357489", "A357849", "A358102" ]
null
Gus Wiseman, Nov 02 2022
2022-11-02T11:52:59
oeisdata/seq/A357/A357849.seq
9b1ecee0aecf55d3f02b5053764a4c8c
A357850
Numbers whose prime indices do not have weakly decreasing run-sums. Heinz numbers of the partitions counted by A357865.
[ "6", "10", "14", "15", "18", "20", "21", "22", "26", "28", "30", "33", "34", "35", "36", "38", "39", "42", "44", "46", "50", "51", "52", "54", "55", "56", "57", "58", "60", "62", "65", "66", "68", "69", "70", "72", "74", "75", "76", "77", "78", "82", "84", "85", "86", "87", "88", "90", "91", "92", "93", "94", "95", "98", "99", "100", "102", "104", "105", "106", "108", "110", "111" ]
[ "nonn" ]
5
1
1
[ "A001221", "A001222", "A056239", "A112798", "A118914", "A181819", "A300273", "A304405", "A304406", "A304428", "A304430", "A304442", "A353832", "A353864", "A353932", "A354584", "A357850", "A357861", "A357864", "A357865", "A357875", "A357876", "A357878" ]
null
Gus Wiseman, Oct 19 2022
2022-10-20T12:44:11
oeisdata/seq/A357/A357850.seq
de3e6d579a57d835d06536fb486fc603
A357851
Numbers k such that the half-alternating sum of the prime indices of k is 1.
[ "2", "8", "18", "32", "45", "50", "72", "98", "105", "128", "162", "180", "200", "231", "242", "275", "288", "338", "392", "420", "429", "450", "455", "512", "578", "648", "663", "720", "722", "800", "833", "882", "924", "935", "968", "969", "1050", "1058", "1100", "1125", "1152", "1235", "1250", "1311", "1352", "1458", "1463", "1568", "1680", "1682", "1716" ]
[ "nonn" ]
5
1
1
[ "A000583", "A001105", "A003963", "A035444", "A035544", "A053251", "A055932", "A056239", "A112798", "A316524", "A344616", "A345958", "A351005", "A351006", "A357621", "A357624", "A357625", "A357626", "A357629", "A357630", "A357631", "A357632", "A357633", "A357634", "A357635", "A357636", "A357637", "A357639", "A357640", "A357641", "A357642", "A357643", "A357644", "A357851" ]
null
Gus Wiseman, Oct 28 2022
2022-10-29T09:10:22
oeisdata/seq/A357/A357851.seq
2254d3d9729a5624a262c7196c4a7d99
A357852
Replace prime(k) with prime(k+2) in the prime factorization of n.
[ "1", "5", "7", "25", "11", "35", "13", "125", "49", "55", "17", "175", "19", "65", "77", "625", "23", "245", "29", "275", "91", "85", "31", "875", "121", "95", "343", "325", "37", "385", "41", "3125", "119", "115", "143", "1225", "43", "145", "133", "1375", "47", "455", "53", "425", "539", "155", "59", "4375", "169", "605", "161", "475", "61", "1715", "187", "1625", "203" ]
[ "nonn", "mult" ]
18
1
2
[ "A000040", "A000720", "A003961", "A003964", "A007310", "A056239", "A064988", "A064989", "A066207", "A076610", "A112798", "A215366", "A296150", "A299201", "A357852", "A357977", "A357979", "A357980", "A357983" ]
null
Gus Wiseman, Oct 28 2022
2022-10-30T08:58:09
oeisdata/seq/A357/A357852.seq
e1a83ead5c0a4ea20800941fd0d23203
A357853
Fully multiplicative with a(prime(k)) = A000009(k+1).
[ "1", "1", "2", "1", "2", "2", "3", "1", "4", "2", "4", "2", "5", "3", "4", "1", "6", "4", "8", "2", "6", "4", "10", "2", "4", "5", "8", "3", "12", "4", "15", "1", "8", "6", "6", "4", "18", "8", "10", "2", "22", "6", "27", "4", "8", "10", "32", "2", "9", "4", "12", "5", "38", "8", "8", "3", "16", "12", "46", "4", "54", "15", "12", "1", "10", "8", "64", "6", "20", "6", "76", "4", "89", "18", "8", "8", "12", "10" ]
[ "nonn", "mult" ]
10
1
3
[ "A000009", "A000040", "A000720", "A003961", "A003964", "A056239", "A064988", "A064989", "A076610", "A112798", "A273873", "A296150", "A357852", "A357853", "A357977", "A357978", "A357979", "A357980", "A357982" ]
null
Gus Wiseman, Oct 28 2022
2022-10-28T20:53:02
oeisdata/seq/A357/A357853.seq
b0580d9c3fad0bfee760bc8ba48649f5
A357854
Squarefree numbers with a divisor having the same sum of prime indices as their quotient.
[ "1", "30", "70", "154", "165", "210", "273", "286", "390", "442", "462", "561", "595", "646", "714", "741", "858", "874", "910", "1045", "1155", "1173", "1254", "1326", "1330", "1334", "1495", "1653", "1771", "1794", "1798", "1870", "1938", "2139", "2145", "2294", "2415", "2465", "2470", "2530", "2622", "2639", "2730", "2926", "2945", "2958", "3034" ]
[ "nonn" ]
6
1
2
[ "A001221", "A001222", "A002219", "A033879", "A033880", "A056239", "A064914", "A112798", "A181819", "A235130", "A237194", "A237258", "A276107", "A300061", "A300273", "A319241", "A321144", "A357854", "A357879", "A357975", "A357976" ]
null
Gus Wiseman, Oct 27 2022
2022-10-27T12:48:43
oeisdata/seq/A357/A357854.seq
917bc62bdb16b26c9ed31a6a4a867849
A357855
Number of closed trails starting and ending at a fixed vertex in the complete undirected graph on n labeled vertices.
[ "1", "1", "3", "13", "829", "78441", "622316671", "3001764349333", "5926347237626029593" ]
[ "nonn", "more", "walk" ]
19
1
3
[ "A007082", "A135388", "A232545", "A350028", "A356366", "A357855", "A357856", "A357857", "A357885", "A357886", "A357887" ]
null
Max Alekseyev, Oct 16 2022
2022-10-19T07:12:00
oeisdata/seq/A357/A357855.seq
51bee9d36e681bbe3462ab3454165343
A357856
Number of trails between two fixed distinct vertices in the complete undirected graph on n labeled vertices.
[ "0", "1", "2", "15", "514", "106085", "317848626", "4238195548627", "2617666555119413330" ]
[ "nonn", "more", "walk" ]
15
1
3
[ "A007082", "A135388", "A232545", "A350028", "A356366", "A357855", "A357856", "A357857", "A357885", "A357886", "A357887" ]
null
Max Alekseyev, Oct 16 2022
2022-10-19T07:14:06
oeisdata/seq/A357/A357856.seq
2a20ac66f86cd119e5b687d2e94f8839
A357857
Number of (open and closed) trails in the complete undirected graph on n labeled vertices.
[ "1", "4", "21", "232", "14425", "3653196", "17705858989", "261353065517776", "241809117107232026097" ]
[ "nonn", "more", "walk" ]
17
1
2
[ "A007082", "A135388", "A232545", "A350028", "A356366", "A357855", "A357856", "A357857", "A357885", "A357886", "A357887" ]
null
Max Alekseyev, Oct 16 2022
2022-10-19T07:16:49
oeisdata/seq/A357/A357857.seq
38cbdc8d2114cacae3bfb52df162836e
A357858
Number of integer partitions that can be obtained by iteratively adding and multiplying together parts of the integer partition with Heinz number n.
[ "1", "1", "1", "3", "1", "3", "1", "6", "2", "3", "1", "7", "1", "3", "3", "11", "1", "7", "1", "8", "3", "3", "1", "14", "3", "3", "4", "8", "1", "11", "1", "19", "3", "3", "3", "18", "1", "3", "3", "18", "1", "12", "1", "8", "8", "3", "1", "27", "3", "10", "3", "8", "1", "16", "3", "19", "3", "3", "1", "25", "1", "3", "8", "33", "3", "12", "1", "8", "3", "12", "1", "35", "1", "3", "11", "8", "3", "12", "1", "34", "9" ]
[ "nonn" ]
7
1
4
[ "A000041", "A000792", "A001055", "A001221", "A001222", "A001970", "A005520", "A048249", "A056239", "A063834", "A066739", "A066815", "A318948", "A319841", "A319850", "A319855", "A319856", "A319909", "A319910", "A319913", "A357858" ]
null
Gus Wiseman, Oct 17 2022
2022-10-17T12:32:10
oeisdata/seq/A357/A357858.seq
611c804725e7adf027f420ea4460a5a0
A357859
Number of integer factorizations of 2n into distinct even factors.
[ "1", "1", "1", "2", "1", "2", "1", "2", "1", "2", "1", "3", "1", "2", "1", "3", "1", "2", "1", "3", "1", "2", "1", "5", "1", "2", "1", "3", "1", "3", "1", "4", "1", "2", "1", "4", "1", "2", "1", "5", "1", "3", "1", "3", "1", "2", "1", "7", "1", "2", "1", "3", "1", "3", "1", "5", "1", "2", "1", "6", "1", "2", "1", "5", "1", "3", "1", "3", "1", "3", "1", "7", "1", "2", "1", "3", "1", "3", "1", "7", "1", "2", "1", "6", "1", "2", "1" ]
[ "nonn" ]
6
1
4
[ "A000005", "A000009", "A000688", "A000961", "A001055", "A001221", "A001222", "A001414", "A004280", "A023894", "A050361", "A295935", "A318721", "A340785", "A357859", "A357860" ]
null
Gus Wiseman, Oct 17 2022
2022-10-17T12:32:15
oeisdata/seq/A357/A357859.seq
abe674688d4a9d997f7e6ed84ab21341
A357860
Number of integer factorizations of n into distinct even factors.
[ "1", "1", "0", "1", "0", "1", "0", "2", "0", "1", "0", "2", "0", "1", "0", "2", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "1", "0", "5", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "3", "0", "1", "0", "4", "0", "1", "0", "2", "0", "1", "0", "4", "0", "1", "0", "2", "0", "1", "0", "5", "0", "1", "0", "3", "0", "1", "0" ]
[ "nonn" ]
6
1
8
[ "A000005", "A000009", "A000688", "A000961", "A001055", "A001221", "A001222", "A001414", "A023894", "A050361", "A295935", "A318721", "A340785", "A349906", "A357859", "A357860" ]
null
Gus Wiseman, Oct 17 2022
2022-10-23T23:55:40
oeisdata/seq/A357/A357860.seq
ed7ebe2734075072587673ead396d79a
A357861
Numbers whose prime indices have weakly decreasing run-sums. Heinz numbers of the partitions counted by A304406.
[ "1", "2", "3", "4", "5", "7", "8", "9", "11", "12", "13", "16", "17", "19", "23", "24", "25", "27", "29", "31", "32", "37", "40", "41", "43", "45", "47", "48", "49", "53", "59", "61", "63", "64", "67", "71", "73", "79", "80", "81", "83", "89", "96", "97", "101", "103", "107", "109", "112", "113", "121", "125", "127", "128", "131", "135", "137", "139", "144", "149", "151", "157" ]
[ "nonn" ]
9
1
2
[ "A001221", "A001222", "A047966", "A056239", "A112798", "A118914", "A181819", "A239312", "A300273", "A304405", "A304406", "A304430", "A304442", "A354584", "A357850", "A357861", "A357864", "A357865", "A357875", "A357876" ]
null
Gus Wiseman, Oct 19 2022
2022-10-20T12:44:21
oeisdata/seq/A357/A357861.seq
1ce4f5471e0e721d51aefe224eb9c1bd
A357862
Numbers whose prime indices have strictly increasing run-sums. Heinz numbers of the partitions counted by A304428.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "41", "42", "43", "44", "46", "47", "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "59", "61", "62", "64", "65", "66", "67", "68", "69", "70", "71", "72", "73", "74" ]
[ "nonn" ]
5
1
2
[ "A001221", "A001222", "A056239", "A112798", "A118914", "A181819", "A275870", "A300273", "A304405", "A304428", "A304430", "A304442", "A354584", "A357862", "A357863", "A357864", "A357875" ]
null
Gus Wiseman, Oct 19 2022
2022-10-20T16:27:04
oeisdata/seq/A357/A357862.seq
0fb807b1697678410c743328c7a071a2
A357863
Numbers whose prime indices do not have strictly increasing run-sums. Heinz numbers of the partitions not counted by A304428.
[ "12", "24", "40", "45", "48", "60", "63", "80", "84", "90", "96", "112", "120", "126", "132", "135", "144", "156", "160", "168", "175", "180", "189", "192", "204", "224", "228", "240", "252", "264", "270", "275", "276", "280", "288", "297", "300", "312", "315", "320", "325", "336", "348", "350", "351", "352", "360", "372", "378", "384", "405", "408", "420", "440" ]
[ "nonn" ]
5
1
1
[ "A001221", "A001222", "A056239", "A112798", "A118914", "A181819", "A300273", "A304428", "A304430", "A304442", "A354584", "A357862", "A357863", "A357864", "A357875", "A357876", "A357878" ]
null
Gus Wiseman, Oct 19 2022
2022-10-20T12:45:03
oeisdata/seq/A357/A357863.seq
e38681f7da7b2c8bf9ba81a3be2242a6
A357864
Numbers whose prime indices have strictly decreasing run-sums. Heinz numbers of the partitions counted by A304430.
[ "1", "2", "3", "4", "5", "7", "8", "9", "11", "13", "16", "17", "19", "23", "24", "25", "27", "29", "31", "32", "37", "41", "43", "45", "47", "48", "49", "53", "59", "61", "64", "67", "71", "73", "79", "80", "81", "83", "89", "96", "97", "101", "103", "107", "109", "113", "121", "125", "127", "128", "131", "135", "137", "139", "149", "151", "157", "160", "163", "167", "169", "173" ]
[ "nonn" ]
7
1
2
[ "A001221", "A001222", "A056239", "A112798", "A118914", "A181819", "A300273", "A304405", "A304406", "A304428", "A304430", "A304442", "A304686", "A354584", "A357861", "A357862", "A357863", "A357864", "A357875" ]
null
Gus Wiseman, Oct 19 2022
2022-10-20T13:12:07
oeisdata/seq/A357/A357864.seq
dec56b2e547d45906f225247cbc6578e
A357865
Number of integer partitions of n whose run-sums are not weakly increasing.
[ "0", "0", "0", "1", "1", "4", "5", "10", "13", "22", "31", "45", "57", "85", "115", "155", "199", "267", "344", "452", "577", "744", "940", "1191", "1486", "1877", "2339", "2910", "3595", "4442", "5453", "6688", "8162", "9960", "12089", "14662", "17698", "21365", "25703", "30869", "36961", "44207", "52728", "62801", "74644", "88587", "104930", "124113" ]
[ "nonn" ]
8
0
6
[ "A000009", "A000041", "A047966", "A098859", "A239312", "A275870", "A304405", "A304406", "A304428", "A304430", "A304442", "A353832", "A353837", "A353864", "A354584", "A357850", "A357861", "A357865", "A357875", "A357876", "A357878" ]
null
Gus Wiseman, Oct 19 2022
2022-10-20T12:44:26
oeisdata/seq/A357/A357865.seq
a25fb108ab464a92712bd57ce94c7157
A357866
a(n) is the greatest remainder of n divided by its sum of digits in any base > 1.
[ "0", "0", "1", "0", "2", "0", "3", "2", "4", "2", "5", "2", "6", "4", "7", "4", "8", "4", "9", "6", "10", "6", "11", "6", "12", "8", "13", "8", "14", "8", "15", "10", "16", "10", "17", "10", "18", "12", "19", "12", "20", "12", "21", "14", "22", "14", "23", "14", "24", "16", "25", "16", "26", "16", "27", "18", "28", "18", "29", "18", "30", "20", "31", "20", "32", "20", "33", "22", "34", "22", "35" ]
[ "nonn", "base" ]
10
1
5
[ "A138530", "A357823", "A357866" ]
null
Rémy Sigrist, Oct 17 2022
2022-10-21T06:59:29
oeisdata/seq/A357/A357866.seq
d62ea31de6b1532319a2d41bc5d6786b
A357867
Numbers k such that A334499(k) is not divisible by k.
[ "12", "15", "25", "28", "30", "39" ]
[ "nonn", "more" ]
5
1
1
[ "A334499", "A334500", "A357867" ]
null
Pontus von Brömssen, Oct 17 2022
2022-10-21T10:04:05
oeisdata/seq/A357/A357867.seq
4e23bf5ded60ed3e994e55c600621ba4
A357868
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} (k*j)!* Stirling2(n,k*j).
[ "1", "1", "0", "1", "1", "0", "1", "0", "3", "0", "1", "0", "2", "13", "0", "1", "0", "0", "6", "75", "0", "1", "0", "0", "6", "38", "541", "0", "1", "0", "0", "0", "36", "270", "4683", "0", "1", "0", "0", "0", "24", "150", "2342", "47293", "0", "1", "0", "0", "0", "0", "240", "1260", "23646", "545835", "0", "1", "0", "0", "0", "0", "120", "1560", "16926", "272918", "7087261", "0", "1", "0", "0", "0", "0", "0", "1800", "8400", "197316", "3543630", "102247563", "0" ]
[ "nonn", "tabl" ]
16
0
9
[ "A000007", "A000670", "A052841", "A324162", "A353774", "A353775", "A357293", "A357868", "A357869", "A357881" ]
null
Seiichi Manyama, Oct 17 2022
2022-10-18T13:31:43
oeisdata/seq/A357/A357868.seq
731b681244948acae7045d0c176be100
A357869
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} (k*j)!* Stirling2(n,k*j)/j!.
[ "1", "1", "0", "1", "1", "0", "1", "0", "2", "0", "1", "0", "2", "5", "0", "1", "0", "0", "6", "15", "0", "1", "0", "0", "6", "26", "52", "0", "1", "0", "0", "0", "36", "150", "203", "0", "1", "0", "0", "0", "24", "150", "962", "877", "0", "1", "0", "0", "0", "0", "240", "900", "6846", "4140", "0", "1", "0", "0", "0", "0", "120", "1560", "9366", "54266", "21147", "0", "1", "0", "0", "0", "0", "0", "1800", "8400", "101556", "471750", "115975", "0" ]
[ "nonn", "tabl" ]
18
0
9
[ "A000007", "A000110", "A052859", "A324162", "A353664", "A353665", "A357293", "A357868", "A357869" ]
null
Seiichi Manyama, Oct 17 2022
2024-01-05T12:29:43
oeisdata/seq/A357/A357869.seq
2831200e182c55e363209eafd704b504
A357870
Triangle of integers related to generalized Markov numbers, read by rows.
[ "3", "13", "51", "61", "217", "846", "291", "1001", "3673", "14637", "1393", "4683", "16693", "62221", "247965", "6673", "22265", "77064", "282317", "1054081", "4200768", "31971", "106153", "360517", "1285131", "4778353", "17857153", "71165091" ]
[ "nonn", "tabl", "more" ]
18
1
1
[ "A101368", "A357749", "A357870" ]
null
Michel Marcus, Oct 17 2022
2022-10-19T06:47:58
oeisdata/seq/A357/A357870.seq
3ffc016cd1bad9edb7161e8f212587ed
A357871
Total number of n-multisets of semi-Dyck paths from (0,0) to (n,n-2*j) for j=0..floor(n/2).
[ "1", "1", "2", "5", "21", "183", "3424", "155833", "25962389", "10152021001", "18355563410823", "94826525443572702", "1720192707342762602561", "135432808172830648285721490", "25492564910167901918236137649748", "28315683468644276652408152922412713937", "65407605920313732627652296139090181364409413" ]
[ "nonn" ]
25
0
3
[ "A008315", "A357825", "A357871" ]
null
Alois P. Heinz, Oct 17 2022
2022-11-19T03:36:59
oeisdata/seq/A357/A357871.seq
99af406612f841bc42fa796b06484e09
A357872
a(n) = n * (3/2)^(v(n, 2) - v(n, 3)) where v(n, k) = valuation(n, k) mod 2 for n > 0.
[ "1", "3", "2", "4", "5", "6", "7", "12", "9", "15", "11", "8", "13", "21", "10", "16", "17", "27", "19", "20", "14", "33", "23", "24", "25", "39", "18", "28", "29", "30", "31", "48", "22", "51", "35", "36", "37", "57", "26", "60", "41", "42", "43", "44", "45", "69", "47", "32", "49", "75", "34", "52", "53", "54", "55", "84", "38", "87", "59", "40", "61", "93", "63", "64", "65", "66", "67", "68", "46", "105", "71", "108", "73", "111" ]
[ "nonn", "easy", "mult" ]
30
1
2
[ "A007814", "A007949", "A064614", "A096268", "A182581", "A357872" ]
null
Werner Schulte, Oct 17 2022
2023-12-10T09:22:53
oeisdata/seq/A357/A357872.seq
6afec26cc0cb60a11b07b4c28e5c8122
A357873
Numbers whose multiset of prime factors has all non-isomorphic multiset partitions.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "31", "32", "33", "34", "35", "37", "38", "39", "40", "41", "43", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "59", "61", "62", "63", "64", "65", "67", "68", "69", "71", "72", "73" ]
[ "nonn" ]
7
1
2
[ "A000612", "A001055", "A001221", "A001222", "A007716", "A055621", "A056239", "A112798", "A283877", "A302545", "A317533", "A317791", "A321194", "A357873", "A357874" ]
null
Gus Wiseman, Oct 18 2022
2022-10-18T13:32:12
oeisdata/seq/A357/A357873.seq
cece4fe51f283a1f04f37b9c73481ce0
A357874
Numbers whose multiset of prime factors has at least two multiset partitions that are isomorphic.
[ "30", "36", "42", "60", "66", "70", "78", "84", "90", "100", "102", "105", "110", "114", "120", "126", "130", "132", "138", "140", "150", "154", "156", "165", "168", "170", "174", "180", "182", "186", "190", "195", "196", "198", "204", "210", "216", "220", "222", "225", "228", "230", "231", "234", "238", "240", "246", "252", "255", "258", "260", "264", "266", "270" ]
[ "nonn" ]
6
1
1
[ "A000612", "A001055", "A001221", "A001222", "A007716", "A055621", "A056239", "A112798", "A283877", "A300913", "A302545", "A317533", "A317791", "A321194", "A357873", "A357874" ]
null
Gus Wiseman, Oct 18 2022
2022-10-18T13:32:06
oeisdata/seq/A357/A357874.seq
4bc576bc5882054b7d628c22deec1c63
A357875
Numbers whose run-sums of prime indices are weakly increasing.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "46", "47", "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66", "67", "68", "69", "70" ]
[ "nonn" ]
4
1
2
[ "A001221", "A001222", "A047966", "A056239", "A112798", "A118914", "A181819", "A239312", "A275870", "A300273", "A304405", "A304442", "A325249", "A353743", "A354584", "A354912", "A357875", "A357876" ]
null
Gus Wiseman, Oct 18 2022
2022-10-18T13:32:32
oeisdata/seq/A357/A357875.seq
08dd1c37201c012f7348a58996a11688
A357876
The run-sums of the prime indices of n are not weakly increasing.
[ "24", "45", "48", "80", "90", "96", "120", "135", "160", "168", "175", "180", "189", "192", "224", "240", "264", "270", "275", "288", "297", "312", "315", "320", "336", "350", "360", "378", "384", "405", "408", "448", "456", "480", "495", "525", "528", "539", "540", "550", "552", "560", "567", "576", "585", "594", "600", "624", "630", "637", "640", "672", "696" ]
[ "nonn" ]
8
1
1
[ "A001221", "A001222", "A047966", "A056239", "A112798", "A118914", "A181819", "A239312", "A275870", "A300273", "A304442", "A325249", "A353743", "A354584", "A354912", "A357875", "A357876", "A357878" ]
null
Gus Wiseman, Oct 17 2022
2022-10-18T07:27:35
oeisdata/seq/A357/A357876.seq
793eef5c72c7a63372368a59f175c63a
A357877
The a(n)-th composition in standard order is the sequence of run-sums of the prime indices of n.
[ "0", "1", "2", "2", "4", "6", "8", "4", "8", "12", "16", "10", "32", "24", "20", "8", "64", "24", "128", "20", "40", "48", "256", "18", "32", "96", "32", "40", "512", "52", "1024", "16", "80", "192", "72", "40", "2048", "384", "160", "36", "4096", "104", "8192", "80", "68", "768", "16384", "34", "128", "96", "320", "160", "32768", "96", "144", "72", "640", "1536", "65536", "84" ]
[ "nonn" ]
9
1
3
[ "A001221", "A001222", "A011782", "A047966", "A056239", "A066099", "A112798", "A118914", "A181819", "A238279", "A239312", "A275870", "A300273", "A304405", "A304442", "A304660", "A329738", "A333755", "A351014", "A353743", "A353832", "A353847", "A354584", "A354912", "A357875", "A357877" ]
null
Gus Wiseman, Oct 17 2022
2023-07-15T10:36:14
oeisdata/seq/A357/A357877.seq
16d9e05bb9aded590cab5b28642f8df4
A357878
Number of integer partitions of n whose run-sums are not weakly decreasing.
[ "0", "0", "0", "0", "0", "1", "1", "3", "4", "8", "11", "19", "25", "40", "55", "79", "104", "150", "196", "270", "350", "467", "600", "786", "997", "1293", "1632", "2077", "2597", "3283", "4067", "5088", "6268", "7769", "9517", "11704", "14238", "17405", "21092", "25598", "30861", "37278", "44729", "53742", "64226", "76811", "91448", "108929", "129174" ]
[ "nonn" ]
6
0
8
[ "A000009", "A000041", "A047966", "A098859", "A239312", "A275870", "A304405", "A304406", "A304428", "A304430", "A304442", "A353832", "A353837", "A353864", "A353932", "A354584", "A357850", "A357865", "A357875", "A357876", "A357878" ]
null
Gus Wiseman, Oct 18 2022
2022-10-20T12:44:31
oeisdata/seq/A357/A357878.seq
bb9dab816c2afe7118228c236f6cc1fd
A357879
Number of divisors of n with the same sum of prime indices as their quotient. Central column of A321144, taking gaps as 0's.
[ "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "2", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "1", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "2", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "2", "1", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "2", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "2" ]
[ "nonn" ]
12
1
12
[ "A001221", "A001222", "A002219", "A033879", "A033880", "A056239", "A064914", "A112798", "A181819", "A213074", "A235130", "A237258", "A276107", "A300061", "A321144", "A357879", "A357975", "A357976" ]
null
Gus Wiseman, Oct 27 2022
2025-01-20T22:52:24
oeisdata/seq/A357/A357879.seq
9c252d8d1837821ddecd8ee2f816921b
A357880
a(1) = a(2) = 1; for n > 2, a(n) is the smallest positive number such that a(n) plus the sum of all previous terms appears in the string concatenation of a(1)..a(n-1).
[ "1", "1", "9", "8", "79", "21", "79", "19", "574", "1", "87", "40", "2", "36", "30", "211", "593", "83", "83", "30", "128", "64", "184", "501", "148", "9", "280", "329", "203", "5", "185", "161", "3", "314", "391", "119", "150", "24", "556", "197", "195", "64", "105", "108", "8", "777", "207", "16", "302", "52", "147", "2", "111", "298", "53", "67", "66", "20", "105", "99", "37", "15", "85", "51", "183", "39", "45", "8", "14" ]
[ "nonn", "base" ]
12
1
3
[ "A000027", "A000217", "A007908", "A337227", "A351753", "A357432", "A357433", "A357880" ]
null
Scott R. Shannon, Oct 18 2022
2022-10-20T20:37:27
oeisdata/seq/A357/A357880.seq
7079abe624aceb86bcf6138a54959f1c
A357881
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} (k*j)!* |Stirling1(n,k*j)|.
[ "1", "1", "0", "1", "1", "0", "1", "0", "3", "0", "1", "0", "2", "14", "0", "1", "0", "0", "6", "88", "0", "1", "0", "0", "6", "46", "694", "0", "1", "0", "0", "0", "36", "340", "6578", "0", "1", "0", "0", "0", "24", "210", "3308", "72792", "0", "1", "0", "0", "0", "0", "240", "2070", "36288", "920904", "0", "1", "0", "0", "0", "0", "120", "2040", "24864", "460752", "13109088", "0", "1", "0", "0", "0", "0", "0", "1800", "17640", "310632", "6551424", "207360912", "0" ]
[ "nonn", "tabl" ]
16
0
9
[ "A000007", "A007840", "A052811", "A353118", "A353119", "A353200", "A357119", "A357868", "A357881", "A357882" ]
null
Seiichi Manyama, Oct 18 2022
2022-10-18T13:31:56
oeisdata/seq/A357/A357881.seq
eb80387090321dd7caf01157647efd80
A357882
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} (k*j)!* |Stirling1(n,k*j)|/j!.
[ "1", "1", "0", "1", "1", "0", "1", "0", "2", "0", "1", "0", "2", "6", "0", "1", "0", "0", "6", "24", "0", "1", "0", "0", "6", "34", "120", "0", "1", "0", "0", "0", "36", "220", "720", "0", "1", "0", "0", "0", "24", "210", "1688", "5040", "0", "1", "0", "0", "0", "0", "240", "1710", "14868", "40320", "0", "1", "0", "0", "0", "0", "120", "2040", "17304", "147684", "362880", "0", "1", "0", "0", "0", "0", "0", "1800", "17640", "194712", "1631376", "3628800", "0" ]
[ "nonn", "tabl" ]
17
0
9
[ "A000007", "A000142", "A009199", "A353344", "A353358", "A353404", "A357119", "A357869", "A357881", "A357882" ]
null
Seiichi Manyama, Oct 18 2022
2022-10-19T11:11:39
oeisdata/seq/A357/A357882.seq
9e6a15772bcac09a2c90190921bbec1a
A357883
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} (k*j)!* |Stirling1(n,k*j)|/(k!^j * j!).
[ "1", "1", "0", "1", "1", "0", "1", "0", "2", "0", "1", "0", "1", "6", "0", "1", "0", "0", "3", "24", "0", "1", "0", "0", "1", "14", "120", "0", "1", "0", "0", "0", "6", "80", "720", "0", "1", "0", "0", "0", "1", "35", "544", "5040", "0", "1", "0", "0", "0", "0", "10", "235", "4284", "40320", "0", "1", "0", "0", "0", "0", "1", "85", "1834", "38310", "362880", "0", "1", "0", "0", "0", "0", "0", "15", "735", "16352", "383256", "3628800", "0" ]
[ "nonn", "tabl" ]
14
0
9
[ "A000007", "A000142", "A324162", "A347001", "A347002", "A347003", "A347004", "A357119", "A357881", "A357882", "A357883" ]
null
Seiichi Manyama, Oct 18 2022
2022-10-18T13:31:38
oeisdata/seq/A357/A357883.seq
ca3d0791d0de56acfaee765e32f90e37
A357884
a(1)=0; if a(n-1) shares any digits with n-1, then a(n) = a(n-1) with all copies of digits from n-1 removed. Otherwise, a(n) = a(n-1) + (n-1).
[ "0", "1", "3", "0", "4", "9", "15", "22", "30", "39", "49", "60", "72", "85", "99", "114", "4", "21", "2", "21", "1", "0", "22", "0", "24", "4", "30", "57", "85", "114", "144", "44", "76", "109", "143", "14", "50", "87", "7", "46", "6", "47", "7", "50", "94", "9", "55", "102", "150", "199", "249", "300", "352", "2", "56", "6", "0", "57", "7", "66", "0", "61", "1", "64", "0", "65", "5" ]
[ "nonn", "base", "easy", "look" ]
43
1
3
[ "A045541", "A357884" ]
null
Gavin Lupo, Oct 18 2022
2022-10-29T07:06:31
oeisdata/seq/A357/A357884.seq
036738b97f0226eab7585d9d1e5d952f
A357885
Triangle read by rows: T(n,k) = number of closed trails of length k starting and ending at a fixed vertex in the complete undirected graph on n labeled vertices, for n >= 1 and k = 0 .. n(n-1)/2.
[ "1", "1", "0", "1", "0", "0", "2", "1", "0", "0", "6", "6", "0", "0", "1", "0", "0", "12", "24", "24", "72", "168", "0", "0", "528", "1", "0", "0", "20", "60", "120", "480", "1680", "3120", "5760", "15840", "29040", "22320", "0", "0", "0", "1", "0", "0", "30", "120", "360", "1800", "8280", "27360", "88560", "310320", "934560", "2296800", "5541120", "12965760", "21837600", "27740160", "58752000", "101882880", "0", "0", "389928960" ]
[ "tabf", "nonn", "walk" ]
12
1
7
[ "A007082", "A135388", "A232545", "A350028", "A356366", "A357855", "A357856", "A357857", "A357885", "A357886", "A357887" ]
null
Max Alekseyev, Oct 18 2022
2022-10-21T14:30:40
oeisdata/seq/A357/A357885.seq
a64f21633228c92a49129d0064b3cd9a
A357886
Triangle read by rows: T(n,k) = number of open trails of length k starting and ending at fixed distinct vertices in the complete undirected graph on n labeled vertices, for n >= 1 and k = 0 .. n*(n-1)/2.
[ "0", "0", "1", "0", "1", "1", "0", "0", "1", "2", "2", "4", "6", "0", "0", "1", "3", "6", "18", "48", "78", "96", "132", "132", "0", "0", "1", "4", "12", "48", "180", "528", "1392", "3600", "7920", "13680", "21840", "31872", "25008", "0", "0", "0", "1", "5", "20", "100", "480", "1980", "7680", "29040", "100920", "316320", "923520", "2502000", "6011760", "12584880", "23417280", "38196480", "50112000", "53667840", "64988160", "64988160", "0" ]
[ "tabf", "nonn", "walk" ]
14
1
10
[ "A007082", "A135388", "A232545", "A350028", "A356366", "A357855", "A357856", "A357857", "A357885", "A357886", "A357887" ]
null
Max Alekseyev, Oct 19 2022
2022-10-22T08:08:02
oeisdata/seq/A357/A357886.seq
5fa2fe70ad1383ef8ad078c1b387c614
A357887
Triangle read by rows: T(n,k) = number of circuits of length k in the complete undirected graph on n labeled vertices, for n >= 1 and k = 0 .. n(n-1)/2.
[ "1", "2", "0", "3", "0", "0", "2", "4", "0", "0", "8", "6", "0", "0", "5", "0", "0", "20", "30", "24", "60", "120", "0", "0", "264", "6", "0", "0", "40", "90", "144", "480", "1440", "2340", "3840", "9504", "15840", "11160", "0", "0", "0", "7", "0", "0", "70", "210", "504", "2100", "8280", "23940", "68880", "217224", "594720", "1339800", "2983680", "6482880", "10190880", "12136320", "24192000", "39621120", "0", "0", "129976320" ]
[ "tabf", "nonn", "walk" ]
17
1
2
[ "A007082", "A135388", "A232545", "A350028", "A356366", "A357855", "A357856", "A357857", "A357885", "A357886", "A357887" ]
null
Max Alekseyev, Oct 19 2022
2022-10-21T14:31:54
oeisdata/seq/A357/A357887.seq
07b126bab3c41225475d1b01a65f2823
A357888
a(n) is the minimal squared length of the longest side of a strictly convex grid n-gon of smallest area.
[ "2", "1", "2", "2", "5", "2", "5", "5", "5", "5", "10", "5", "10", "5", "13", "10", "13", "10", "13", "13", "17", "13", "17", "13", "25", "17", "25", "17", "25", "13", "25", "17", "26", "17", "26", "17", "26", "17", "26", "25", "26", "25", "29", "29", "29", "34", "34", "34", "41", "37", "41", "37", "41", "34", "41", "41", "41", "41", "41", "41", "61", "41", "61", "41", "61", "41", "61", "41", "41" ]
[ "nonn" ]
31
3
1
[ "A063984", "A070911", "A089187", "A321693", "A322029", "A322345", "A322348", "A357888" ]
null
Hugo Pfoertner, Nov 10 2022
2025-01-01T22:19:19
oeisdata/seq/A357/A357888.seq
9405651f9ec14ecda1af85bc560f4605
A357889
a(n) = (A022010(n) - 179)/210.
[ "26", "422", "1355", "2983", "4074", "5460", "31242", "35906", "40825", "84968", "90902", "114293", "204675", "207304", "329316", "353648", "377182", "382985", "400497", "418993", "590790", "611757", "686734", "748244", "993947", "1038255", "1181931", "1246060", "1310026", "1347976", "1354707", "1440679", "1477788", "1559980", "1720425", "1915719", "1989590" ]
[ "nonn" ]
10
1
1
[ "A022009", "A022010", "A182387", "A357889", "A357890" ]
null
Hugo Pfoertner, Nov 18 2022
2022-11-18T20:09:02
oeisdata/seq/A357/A357889.seq
68c39bab40e994fd18bcefe5bddc8408
A357890
a(n) = (A022013(n) - 173)/210.
[ "422", "1355", "4074", "5460", "31242", "329316", "353648", "1038255", "1246060", "1440679", "4593664", "6382389", "6669205", "6773694", "8748381", "9343041", "10085055", "10711252", "10819136", "12181959", "12804411", "13683806", "14044105", "15616253", "19232028", "20795482", "21014272", "25076295", "26366476", "27457318" ]
[ "nonn" ]
8
1
1
[ "A022011", "A022012", "A022013", "A145315", "A182393", "A357889", "A357890" ]
null
Hugo Pfoertner, Nov 18 2022
2022-11-18T20:08:57
oeisdata/seq/A357/A357890.seq
4bd4f8789b53cc4489e0c706033b8144
A357891
a(1) = 1; a(n+1) is the smallest integer > 0 that cannot be obtained from the integers {a(1), ..., a(n)} using each number exactly once and the operators +, -, *, /.
[ "1", "2", "4", "11", "34", "152", "1079", "6610", "93221" ]
[ "nonn", "hard", "more" ]
11
1
2
[ "A071115", "A217043", "A357891", "A358075" ]
null
Rainer Rosenthal and Hugo Pfoertner, Nov 01 2022
2022-11-10T12:35:59
oeisdata/seq/A357/A357891.seq
925a4e511e7bbb75b0b1e0e0c51e9627
A357892
T(n,k) are the values of a variant of the Chebyshev polynomials P(n,x) of order n evaluated at x = k, where T(n,k), n >= 0, k <= n is a triangle read by rows. P(0,x) = 1, P(1,x) = x, P(n,x) = x*P(n-1,x) - P(n-2,x).
[ "1", "0", "1", "-1", "0", "3", "0", "-1", "4", "21", "1", "-1", "5", "55", "209", "0", "0", "6", "144", "780", "2640", "-1", "1", "7", "377", "2911", "12649", "40391", "0", "1", "8", "987", "10864", "60605", "235416", "726103", "1", "0", "9", "2584", "40545", "290376", "1372105", "4976784", "15003009", "0", "-1", "10", "6765", "151316", "1391275", "7997214", "34111385", "118118440", "350382231" ]
[ "sign", "tabl" ]
6
0
6
[ "A001353", "A001906", "A097690", "A357892" ]
null
Hugo Pfoertner, Oct 18 2022
2022-10-19T06:49:13
oeisdata/seq/A357/A357892.seq
f6c703eacfa7a963afc48548dead24f6
A357893
a(d) is the minimal integer k such that all Jensen polynomials Jd,nPL(x) associated to MacMahon's plane partition function PL(n) have real roots for x >= k.
[ "12", "26", "46", "73", "102", "136" ]
[ "nonn", "more" ]
9
2
1
[ "A324794", "A357893" ]
null
Michel Marcus, Oct 18 2022
2022-10-21T14:33:38
oeisdata/seq/A357/A357893.seq
e5d5b7dbd3a288f102dd5813d50080f1
A357894
Integers k such that the sum of some number of initial decimal digits of sqrt(k) is equal to k.
[ "0", "1", "6", "10", "14", "18", "27", "33", "41", "43", "46", "55", "56", "62", "66", "69", "70", "77", "80", "87", "93", "98", "102", "108", "110", "123", "124", "145", "147", "149", "150", "154", "157", "162", "164", "165", "168", "176", "177", "179", "180", "182", "183", "197", "204", "213", "214", "219", "224", "236", "237", "242", "248", "251", "252", "261", "262", "263", "271", "274", "285", "295" ]
[ "nonn", "base" ]
19
1
3
[ "A106039", "A357894" ]
null
Gil Broussard, Oct 18 2022
2022-11-19T21:22:26
oeisdata/seq/A357/A357894.seq
3010465abed3840bd4805d3fe95de4ad
A357895
Number of partitions of the complete graph on n vertices into strokes.
[ "1", "2", "12", "472", "104800" ]
[ "nonn", "more", "walk" ]
8
1
2
[ "A089243", "A131518", "A131520", "A131709", "A354228", "A357857", "A357895" ]
null
Yasutoshi Kohmoto and Max Alekseyev, Oct 18 2022
2022-10-21T14:32:24
oeisdata/seq/A357/A357895.seq
0287273d91984b0c1d985b01f5419373
A357896
Additive triprimes.
[ "8", "44", "66", "75", "99", "116", "125", "138", "147", "165", "170", "174", "242", "246", "255", "273", "279", "282", "318", "332", "345", "354", "363", "369", "387", "404", "426", "435", "477", "507", "530", "534", "549", "561", "578", "596", "602", "606", "615", "639", "642", "651", "657", "668", "705", "710", "741", "747", "822", "873", "903", "909", "927", "938", "956", "963", "981", "1025", "1034", "1038", "1052", "1065", "1070", "1074" ]
[ "nonn", "base" ]
13
1
1
[ "A007953", "A014612", "A046704", "A118688", "A357896" ]
null
Zak Seidov, Oct 18 2022
2022-11-02T07:28:34
oeisdata/seq/A357/A357896.seq
802bc1b1eb3f530f7081b93a92b74542
A357897
a(1)=1; thereafter a(n)=n+k, where k is the minimal value of k such that a(k)=n-1 and k belongs to [1, n-1], or k=0 if no such value exists.
[ "1", "3", "3", "6", "5", "11", "11", "8", "17", "10", "21", "18", "13", "27", "15", "31", "17", "27", "31", "20", "41", "33", "23", "47", "25", "51", "27", "42", "29", "59", "31", "48", "33", "56", "35", "71", "37", "75", "39", "79", "41", "63", "71", "44", "89", "46", "93", "72", "81", "50", "101", "78", "53", "107", "55", "111", "91", "58", "117", "90", "61", "123", "63", "106", "65", "131", "67" ]
[ "nonn" ]
21
1
2
null
null
Joseph Bove, Oct 19 2022
2022-10-24T14:13:50
oeisdata/seq/A357/A357897.seq
a5ca920d705f33200e48fea345cea8df
A357898
a(n) is the least k such that phi(k) + d(k) = 2^n, or -1 if there is no such k, where phi(k) = A000010(k) is Euler's totient function and d(k) = A000005(k) is the number of divisors of k.
[ "1", "3", "7", "21", "31", "77", "127", "301", "783", "1133", "3399", "4781", "8191", "16637", "37367", "101601", "131071", "305837", "524287", "1073581", "3220743", "4201133", "8544103", "18404669", "34012327", "67139117", "135255431", "300528877", "824583699", "1073862029", "2147483647", "4295564381", "8603449703", "25807607829" ]
[ "nonn" ]
43
1
2
[ "A000005", "A000010", "A061468", "A070319", "A073757", "A357898" ]
null
J. M. Bergot and Robert Israel, Oct 19 2022
2023-01-20T21:44:00
oeisdata/seq/A357/A357898.seq
88fb301e60ac85a10411f0a147579ff0
A357899
Let k be the smallest k such that the square root of k*n rounds to a prime number; a(n) is this prime number.
[ "2", "2", "2", "2", "2", "2", "3", "3", "3", "3", "3", "3", "5", "5", "5", "7", "7", "7", "11", "11", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "11", "11", "11", "13", "13", "13", "11", "11", "11", "11", "11", "11", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "23", "23", "17", "17", "17", "17", "17", "17", "17", "17" ]
[ "nonn" ]
13
1
1
[ "A000194", "A308052", "A357477", "A357899" ]
null
Rémy Sigrist, Oct 19 2022
2022-10-19T12:59:02
oeisdata/seq/A357/A357899.seq
f25104071e6d83e7076ead6415293eef
A357900
Number of groups of order A060702(n) with trivial center.
[ "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "2", "1", "2", "2", "1", "5", "1", "1", "1", "1", "3", "1", "1", "1", "1", "6", "1", "1", "2", "1", "1", "2", "1", "2", "1", "1", "5", "2", "5", "1", "1", "5", "2", "1", "2", "1", "1", "4", "1", "4", "1", "1", "1", "1", "1", "1", "2", "1", "3", "1", "3", "1", "4", "1", "1", "4", "1", "1", "17", "1", "1", "5", "1", "1", "1", "1", "8", "1", "1", "2", "1", "11", "1", "2", "2", "5", "1", "1", "1", "2", "1", "1", "3", "1", "1", "19" ]
[ "nonn", "hard" ]
21
1
6
[ "A056867", "A059806", "A060702", "A357900" ]
null
Jianing Song, Oct 19 2022
2022-10-20T07:43:18
oeisdata/seq/A357/A357900.seq
d533c43857f5974497fbbc330ca26ddb