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348
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int64
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2.35k
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int64
-14,827
666,262,453B
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0
635M
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1999-12-11 03:00:00
2025-07-14 02:38:35
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A362901
Number of nonisomorphic unordered triples of fixed-point-free endofunctions on an n-set.
[ "1", "0", "1", "22", "3935", "1497568", "883538845", "725601878962", "792072162839065", "1110677779035583912", "1947266694667001733208", "4175906998639267840682727", "10757238370963150080155796720", "32785728540392233760236496299048", "116709223477757580428169966318431329" ]
[ "nonn" ]
7
0
4
[ "A362899", "A362900", "A362901" ]
null
Andrew Howroyd, May 10 2023
2023-05-10T22:38:49
oeisdata/seq/A362/A362901.seq
9082ae727544238d06d00a71d0fb3a84
A362902
Number of nonisomorphic multisets of fixed-point-free endofunctions on an n-set with n endofunctions.
[ "1", "0", "1", "22", "81015", "78954264778", "28097782272713021650", "5303746708038163087962610366540", "750301169575330570948709311656320180808090293", "107340347538849305728376873042317973326061404804760169389400111", "20170881768834535901905153264317820972982675109510814553304001503205327205300015737" ]
[ "nonn" ]
6
0
4
[ "A277839", "A362899", "A362902" ]
null
Andrew Howroyd, May 10 2023
2023-05-10T22:38:46
oeisdata/seq/A362/A362902.seq
4a99f799245c3fd85928904db2eca25c
A362903
Array read by antidiagonals: T(n,k) is the number of nonisomorphic k-tuples of involutions on a (2n)-set that pairwise commute.
[ "1", "1", "1", "1", "2", "1", "1", "4", "3", "1", "1", "8", "11", "4", "1", "1", "16", "43", "24", "5", "1", "1", "32", "171", "176", "46", "6", "1", "1", "64", "683", "1376", "611", "80", "7", "1", "1", "128", "2731", "10944", "9281", "1864", "130", "8", "1", "1", "256", "10923", "87424", "146445", "54384", "5161", "200", "9", "1", "1", "512", "43691", "699136", "2334181", "1696352", "285939", "13184", "295", "10", "1" ]
[ "nonn", "tabl" ]
12
0
5
[ "A000012", "A000027", "A000079", "A001752", "A007583", "A022166", "A103334", "A362648", "A362824", "A362826", "A362903", "A362904" ]
null
Andrew Howroyd, May 11 2023
2024-10-15T17:29:25
oeisdata/seq/A362/A362903.seq
002ff5202283e82d21a36dd3bfeb24ee
A362904
Number of nonisomorphic ordered triples of involutions on a (2n)-set that pairwise commute.
[ "1", "8", "43", "176", "611", "1864", "5161", "13184", "31532", "71264", "153444", "316608", "629236", "1209312", "2255324", "4093056", "7246690", "12542736", "21262582", "35359456", "57767766", "92832784", "146908290", "229169792", "352721676", "536076640", "805132548", "1195771840", "1757278132" ]
[ "nonn" ]
12
0
2
[ "A362903", "A362904" ]
null
Andrew Howroyd, May 11 2023
2023-06-25T08:55:32
oeisdata/seq/A362/A362904.seq
ce5204e711fd64fc29386a368a0d1b04
A362905
Array read by antidiagonals: T(n,k) is the number of n element multisets of length k vectors over GF(2) that sum to zero.
[ "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "4", "2", "1", "1", "1", "8", "5", "3", "1", "1", "1", "16", "15", "11", "3", "1", "1", "1", "32", "51", "50", "14", "4", "1", "1", "1", "64", "187", "276", "99", "24", "4", "1", "1", "1", "128", "715", "1768", "969", "232", "30", "5", "1", "1", "1", "256", "2795", "12496", "11781", "3504", "429", "45", "5", "1", "1", "1", "512", "11051", "93600", "162877", "73440", "10659", "835", "55", "6", "1" ]
[ "nonn", "tabl" ]
18
0
9
[ "A000012", "A000079", "A004526", "A007581", "A053307", "A054724", "A340030", "A340312", "A362905", "A362906", "A363349", "A363350", "A363351" ]
null
Andrew Howroyd, May 27 2023
2023-11-19T15:56:50
oeisdata/seq/A362/A362905.seq
f1e52b780716d86095ac4901e4eda888
A362906
Number of n element multisets of length 3 vectors over GF(2) that sum to zero.
[ "1", "1", "8", "15", "50", "99", "232", "429", "835", "1430", "2480", "3978", "6372", "9690", "14640", "21318", "30789", "43263", "60280", "82225", "111254", "148005", "195416", "254475", "329095", "420732", "534496", "672452", "841160", "1043460", "1287648", "1577532", "1923465", "2330445", "2811240", "3372291", "4029178" ]
[ "nonn", "easy" ]
14
0
3
[ "A006381", "A362905", "A362906" ]
null
Andrew Howroyd, May 27 2023
2023-11-18T18:08:24
oeisdata/seq/A362/A362906.seq
4cf8d2252948b6a28552289281edd51c
A362907
Number of graphs on n unlabeled nodes with treewidth 3.
[ "0", "0", "0", "0", "1", "6", "53", "501", "5889", "81786" ]
[ "nonn", "hard", "more" ]
19
0
6
[ "A263294", "A362907" ]
null
Martin Rubey, May 09 2023
2023-05-14T12:37:55
oeisdata/seq/A362/A362907.seq
616b69bd4f8d52d3b0e8d22af5bf848a
A362908
Number of graphs on n unlabeled nodes with treewidth 2.
[ "0", "0", "0", "1", "4", "17", "72", "323", "1639", "9203" ]
[ "nonn", "more" ]
9
0
5
[ "A263294", "A362908" ]
null
Martin Rubey, May 09 2023
2023-05-10T12:47:36
oeisdata/seq/A362/A362908.seq
fc011bf8c53e95e36e144ba196fcd660
A362909
a(n) is the smallest number k such that A362881(k) = n.
[ "1", "3", "6", "10", "22", "31", "34", "37", "40", "121", "1035", "1078", "1121", "7607", "9453", "13667", "13729", "50040", "50123", "50206", "615964", "616448", "616932", "617416", "2828280", "2851232", "2874184", "2897136", "5350614", "5583250", "5594326", "17310256", "17312210", "17994974", "18008820", "19051432", "19069162" ]
[ "nonn" ]
60
1
2
[ "A362881", "A362909" ]
null
Samuel Harkness, May 14 2023
2024-12-19T11:45:36
oeisdata/seq/A362/A362909.seq
bb5365ba97ca86d67d9b2a9c142e9924
A362910
Semiprimes p*q for which p <= q < p^3.
[ "4", "6", "9", "10", "14", "15", "21", "25", "33", "35", "39", "49", "51", "55", "57", "65", "69", "77", "85", "91", "95", "115", "119", "121", "133", "143", "145", "155", "161", "169", "185", "187", "203", "205", "209", "215", "217", "221", "235", "247", "253", "259", "265", "287", "289", "295", "299", "301", "305", "319", "323", "329", "335", "341", "355", "361", "365" ]
[ "nonn" ]
50
1
1
[ "A001248", "A001358", "A251728", "A362910" ]
null
Alain Rocchelli, May 10 2023
2025-03-06T08:29:02
oeisdata/seq/A362/A362910.seq
1a44b171c0fa14d4cfe6b8b34337303c
A362911
Expansion of e.g.f. 1/( 1 - (1 + x) * log(1 + x) ).
[ "1", "1", "3", "11", "60", "384", "3062", "27838", "293416", "3447768", "45277392", "651587760", "10254900048", "174557518992", "3203361670896", "62938642659504", "1319693558377728", "29390794198726656", "693223221342879360", "17256288944072200320", "452215395177034040064" ]
[ "nonn" ]
18
0
3
[ "A005727", "A006153", "A305306", "A305307", "A362911", "A362912" ]
null
Seiichi Manyama, May 10 2023
2023-11-11T05:20:27
oeisdata/seq/A362/A362911.seq
d835ec1a2b7ce38ff92765b9db939964
A362912
Expansion of e.g.f. 1/( 1 - (exp(x) - 1) * exp(exp(x) - 1) ).
[ "1", "1", "5", "34", "303", "3371", "45016", "701401", "12490057", "250215916", "5569582777", "136371309999", "3642603629462", "105405416033607", "3284722016179597", "109672448519030698", "3905936524326557659", "147802493781420536423", "5921911678533323178312" ]
[ "nonn" ]
15
0
3
[ "A006153", "A305306", "A347339", "A362911", "A362912" ]
null
Seiichi Manyama, May 10 2023
2023-11-11T06:40:21
oeisdata/seq/A362/A362912.seq
301b8af1571a1e97de44d66de49321bb
A362913
Array of numbers read by upward antidiagonals: leading row lists phi(i), i >= 1 (cf. A000010); the following rows give absolute values of differences of previous row.
[ "1", "0", "1", "1", "1", "2", "0", "1", "0", "2", "1", "1", "2", "2", "4", "0", "1", "2", "0", "2", "2", "1", "1", "0", "2", "2", "4", "6", "0", "1", "2", "2", "0", "2", "2", "4", "1", "1", "2", "0", "2", "2", "0", "2", "6", "0", "1", "2", "0", "0", "2", "0", "0", "2", "4", "1", "1", "0", "2", "2", "2", "4", "4", "4", "6", "10", "0", "1", "2", "2", "0", "2", "4", "0", "4", "0", "6", "4", "1", "1", "0", "2", "0", "0", "2", "2", "2", "2", "2", "8", "12", "0", "1", "2", "2" ]
[ "nonn", "tabl" ]
27
1
6
[ "A000010", "A057000", "A362451", "A362913" ]
null
N. J. A. Sloane, May 09 2023
2023-09-27T15:03:26
oeisdata/seq/A362/A362913.seq
e9c533bb7865a19535e42469e2159fa9
A362914
a(n) = size of largest subset of {1..n} such that no difference between two terms is a prime.
[ "1", "2", "2", "2", "2", "2", "2", "2", "3", "3", "4", "4", "4", "4", "4", "4", "5", "5", "5", "5", "6", "6", "6", "6", "7", "7", "7", "7", "8", "8", "8", "8", "9", "9", "9", "9", "10", "10", "10", "10", "11", "11", "11", "11", "12", "12", "12", "12", "13", "13", "13", "13", "14", "14", "14", "14", "15", "15", "15", "15", "16", "16", "16", "16", "17", "17", "17", "17", "18", "18", "18", "18", "19", "19", "19" ]
[ "nonn" ]
34
1
2
[ "A100719", "A131849", "A362914", "A362915" ]
null
N. J. A. Sloane, May 15 2023
2023-05-18T07:40:02
oeisdata/seq/A362/A362914.seq
4b99346341bef52af0b3ebcdae9f41fa
A362915
a(n) = size of largest subset of {1...n} such that no difference between two terms is a prime + 1.
[ "1", "2", "3", "3", "3", "3", "3", "3", "3", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "5", "6", "6", "6", "6", "6", "6", "6", "6", "6", "7", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "9", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "11", "12", "12", "12", "12", "12", "12", "12" ]
[ "nonn" ]
13
1
2
[ "A100719", "A131849", "A362914", "A362915" ]
null
N. J. A. Sloane, May 15 2023
2023-05-18T07:37:24
oeisdata/seq/A362/A362915.seq
3695ddec9b66aef1a795e874e029e11c
A362916
Least weird number (A006037) with exactly n divisors that are weird numbers, or -1 if no such number exists.
[ "70", "10430", "1554070", "5681270", "34501908070", "1436692670" ]
[ "nonn", "hard", "more" ]
13
1
1
[ "A002975", "A006037", "A362916" ]
null
Amiram Eldar, May 26 2023
2023-05-26T05:47:02
oeisdata/seq/A362/A362916.seq
be0fc283683e8455d18ccc6583ffe0d6
A362917
The part of n to the left of the decimal point in the Dekking-van-Loon-canonical base phi representation of n.
[ "0", "1", "10", "11", "101", "1000", "1010", "1011", "10001", "10010", "10011", "10101", "100000", "100010", "100011", "100101", "101000", "101010", "101011", "1000001", "1000010", "1000011", "1000101", "1001000", "1001010", "1001011", "1010001", "1010010", "1010011", "1010101", "10000000" ]
[ "nonn", "base", "more" ]
29
0
3
[ "A003231", "A105424", "A341722", "A362917", "A362918" ]
null
N. J. A. Sloane, May 26 2023
2023-05-27T14:18:38
oeisdata/seq/A362/A362917.seq
5c24e080ff2ebff2b52e1a9790c6cb0a
A362918
Length of the part of n to the left of the decimal point in the Dekking-van-Loon-canonical base phi representation of n.
[ "1", "1", "2", "2", "3", "4", "4", "4", "5", "5", "5", "5", "6" ]
[ "nonn", "base", "more" ]
12
0
3
[ "A105424", "A341722", "A362917", "A362918" ]
null
N. J. A. Sloane, May 26 2023
2023-05-27T14:09:42
oeisdata/seq/A362/A362918.seq
1a1132ca970ffc70eb5607652e00b7e0
A362919
a(n) is the right portion (reversed) of the base-phi representation of n in Knott's representation which uses the least number of 0's, the most 1's, and in which the right-hand portion is finite.
[ "0", "0", "11", "1111", "1111", "1111", "1110", "111101", "111101", "111101", "111111", "111111", "111111", "111110", "111011", "111011", "111011", "111010", "11110101", "11110101", "11110101", "11110111", "11110111", "11110111", "11110110", "11111101", "11111101", "11111101", "11111111", "11111111", "11111111" ]
[ "nonn", "base" ]
25
0
3
[ "A118240", "A362919", "A362920" ]
null
N. J. A. Sloane, May 27 2023
2023-05-27T15:08:37
oeisdata/seq/A362/A362919.seq
fedc7a62672f1749ba90010bab3adc13
A362920
The Knott base-phi representation of n described in A362919 written as a binary string, omitting the dot.
[ "0", "1", "111", "101111", "111111", "1011111", "1110111", "1010101111", "1011101111", "1101101111", "1110111111", "1111111111", "10101111111", "10111011111", "11010110111", "11011110111", "11101110111", "11111010111", "10101010101111", "10101110101111", "10110110101111", "10111011101111", "10111111101111", "11010111101111", "11011101101111", "11101010111111", "11101110111111", "11110110111111", "11111011111111", "11111111111111", "101010111111111" ]
[ "nonn", "base" ]
3
0
3
[ "A118240", "A362919", "A362920" ]
null
N. J. A. Sloane, May 27 2023
2023-05-27T14:54:12
oeisdata/seq/A362/A362920.seq
4b140acfd055f0be3eefd38ff4dd343a
A362921
The Dekking-van-Loon-canonical base-phi representation of n described in A362917 written as a binary string, omitting the dot.
[ "0", "1", "1001", "1101", "10101", "10001001", "10100001", "10110001", "100010001", "100100101", "100110101", "101010101", "100000101001", "100010001001", "100011001001", "100101001001", "101000100001", "101010000001", "101011000001", "1000001000001", "1000010010001", "1000011010001", "1000101010001", "1001000100101", "1001010000101" ]
[ "nonn", "base", "changed" ]
14
0
3
[ "A341722", "A362917", "A362921" ]
null
N. J. A. Sloane, May 27 2023
2025-07-09T05:01:56
oeisdata/seq/A362/A362921.seq
cb8dcfef25733667128f0666979ac640
A362922
Decimal expansion of cos(2*Pi/7) = sin(3*Pi/14) = A255249/2.
[ "6", "2", "3", "4", "8", "9", "8", "0", "1", "8", "5", "8", "7", "3", "3", "5", "3", "0", "5", "2", "5", "0", "0", "4", "8", "8", "4", "0", "0", "4", "2", "3", "9", "8", "1", "0", "6", "3", "2", "2", "7", "4", "7", "3", "0", "8", "9", "6", "4", "0", "2", "1", "0", "5", "3", "6", "5", "5", "4", "9", "4", "3", "9", "0", "9", "6", "8", "5", "3", "6", "5", "2", "4", "5", "6", "4", "8", "7", "2", "8", "4", "5", "7", "5", "9", "4", "2", "5", "0", "7", "3", "2", "6", "5", "8", "5" ]
[ "nonn", "cons" ]
32
0
1
[ "A073052", "A160389", "A232736", "A255249", "A362922" ]
null
N. J. A. Sloane, Jun 25 2023
2023-06-26T17:39:53
oeisdata/seq/A362/A362922.seq
a1116428edb8cbc59e6c497f4eef02c9
A362923
G.f. = (3*x^4+5*x^2+6*x-7)/(4*x^7+x^4+x^2+x-1).
[ "7", "1", "3", "4", "11", "16", "30", "78", "123", "229", "398", "749", "1334", "2432", "4476", "8149", "14875", "27048", "49395", "89928", "163926", "298806", "544723", "992957", "1809798", "3299141", "6013374", "10961176", "19979572", "36418781", "66383555", "121002704", "220562395", "402037376", "732828030", "1335786398", "2434851947", "4438209941" ]
[ "nonn" ]
14
0
1
[ "A362923", "A364701" ]
null
N. J. A. Sloane, Aug 05 2023
2023-11-14T03:27:15
oeisdata/seq/A362/A362923.seq
2d012942b9b8d3de0fce3211d7ad72c4
A362924
Triangle read by rows: T(n,m), n >= 1, 1 <= m <= n, is number of partitions of the set {1,2,...,n} that have at most one block contained in {1,...,m}.
[ "1", "2", "1", "5", "4", "1", "15", "13", "8", "1", "52", "47", "35", "16", "1", "203", "188", "153", "97", "32", "1", "877", "825", "706", "515", "275", "64", "1", "4140", "3937", "3479", "2744", "1785", "793", "128", "1", "21147", "20270", "18313", "15177", "11002", "6347", "2315", "256", "1", "115975", "111835", "102678", "88033", "68303", "45368", "23073", "6817", "512", "1", "678570", "657423", "610989", "536882", "436297", "316305", "191866", "85475", "20195", "1024", "1" ]
[ "nonn", "tabl", "changed" ]
26
1
2
[ "A000110", "A005493", "A008277", "A078468", "A113547", "A143494", "A362924", "A362925" ]
null
N. J. A. Sloane, Aug 10 2023, based on an email from Don Knuth
2025-07-09T05:02:03
oeisdata/seq/A362/A362924.seq
1602c9f8befb2070d77dd33142f03e18
A362925
Triangle read by rows: T(n,m), n >= 0, 0 <= m <= n, is number of partitions of the set {1,2,...,n} that have at most one block contained in {1,...,m}.
[ "1", "1", "1", "2", "2", "1", "5", "5", "4", "1", "15", "15", "13", "8", "1", "52", "52", "47", "35", "16", "1", "203", "203", "188", "153", "97", "32", "1", "877", "877", "825", "706", "515", "275", "64", "1", "4140", "4140", "3937", "3479", "2744", "1785", "793", "128", "1", "21147", "21147", "20270", "18313", "15177", "11002", "6347", "2315", "256", "1", "115975", "115975", "111835", "102678", "88033", "68303", "45368", "23073", "6817", "512", "1" ]
[ "nonn", "tabl", "changed" ]
36
0
4
[ "A000012", "A000079", "A000110", "A007689", "A040027", "A078468", "A113547", "A362924", "A362925", "A367820", "A383052", "A383053", "A383054" ]
null
N. J. A. Sloane, Aug 10 2023, based on an email from Don Knuth
2025-07-09T05:02:10
oeisdata/seq/A362/A362925.seq
1e6223cca0b1c13251e7c1cf46628c2b
A362926
Triangle read by rows: A113547 without its main diagonal.
[ "1", "1", "2", "1", "4", "5", "1", "8", "13", "15", "1", "16", "35", "47", "52", "1", "32", "97", "153", "188", "203", "1", "64", "275", "515", "706", "825", "877", "1", "128", "793", "1785", "2744", "3479", "3937", "4140", "1", "256", "2315", "6347", "11002", "15177", "18313", "20270", "21147", "1", "512", "6817", "23073", "45368", "68303", "88033", "102678", "111835", "115975", "1", "1024", "20195", "85475", "191866", "316305", "436297", "536882", "610989", "657423", "678570" ]
[ "nonn", "tabl", "changed" ]
15
1
3
[ "A113547", "A362924", "A362926" ]
null
N. J. A. Sloane, Aug 11 2023, based on an email from Don Knuth
2025-07-09T05:02:18
oeisdata/seq/A362/A362926.seq
6d3c6b5f15182ba19fd6e9f2043daf92
A362927
Subtract 2 from the terms of the Kolakoski-(1,3) sequence A064353.
[ "-1", "1", "1", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "1", "-1", "1", "1", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "1", "1", "1", "-1", "1", "1", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "1", "-1", "1", "1", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "1", "1", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "1", "1", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "1", "-1", "1", "1", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "1", "1", "1", "-1", "1", "1", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "1", "-1", "1", "1", "1", "-1", "-1", "-1", "1", "1" ]
[ "sign" ]
6
1
null
[ "A000002", "A064353", "A362927", "A362928", "A362929", "A362930" ]
null
N. J. A. Sloane, Aug 12 2023
2023-08-12T15:52:39
oeisdata/seq/A362/A362927.seq
a5fa982f4179ba1cc1536e78aff194a4
A362928
Subtract 2 from the terms of the Kolakoski-(1,3) sequence A064353 and negate the result.
[ "1", "-1", "-1", "-1", "1", "1", "1", "-1", "-1", "-1", "1", "-1", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "-1", "-1", "1", "-1", "-1", "-1", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "-1", "-1", "1", "-1", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "-1", "-1", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "-1", "-1", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "-1", "-1", "1", "-1", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "-1", "-1", "1", "-1", "-1", "-1", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "-1", "-1", "1", "-1", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "-1" ]
[ "sign" ]
5
1
null
[ "A000002", "A064353", "A362928", "A362929", "A362930" ]
null
N. J. A. Sloane, Aug 12 2023
2023-08-12T15:53:14
oeisdata/seq/A362/A362928.seq
1315c21a9acf76eef9a9f1777cdb36fd
A362929
Indices of 1's in A064353.
[ "1", "5", "6", "7", "11", "13", "17", "18", "19", "23", "27", "31", "32", "33", "37", "39", "43", "44", "45", "49", "53", "54", "55", "59", "63", "64", "65", "69", "71", "75", "76", "77", "81", "85", "89", "90", "91", "95", "97", "101", "102", "103", "107", "111", "112", "113", "117", "119", "123", "124", "125", "129", "133", "134", "135", "139", "141", "145", "146", "147", "151", "155", "159", "160", "161", "165" ]
[ "nonn" ]
5
1
2
[ "A064353", "A362927", "A362928", "A362929", "A362930" ]
null
N. J. A. Sloane, Aug 12 2023
2023-08-12T11:11:05
oeisdata/seq/A362/A362929.seq
ddbf3f458e8936568a946176178af530
A362930
Indices of 3's in A064353.
[ "2", "3", "4", "8", "9", "10", "12", "14", "15", "16", "20", "21", "22", "24", "25", "26", "28", "29", "30", "34", "35", "36", "38", "40", "41", "42", "46", "47", "48", "50", "51", "52", "56", "57", "58", "60", "61", "62", "66", "67", "68", "70", "72", "73", "74", "78", "79", "80", "82", "83", "84", "86", "87", "88", "92", "93", "94", "96", "98", "99", "100", "104", "105", "106", "108", "109", "110", "114", "115", "116", "118" ]
[ "nonn" ]
5
1
1
[ "A064353", "A362927", "A362928", "A362929", "A362930" ]
null
N. J. A. Sloane, Aug 12 2023
2023-08-12T11:11:14
oeisdata/seq/A362/A362930.seq
16cf8d23434e4b8dd6bac8922f4cb82b
A362931
a(n) = number of pairs (i,j) in [1..n] X [1..n] with integral harmonic mean 2*i*j/(i+j).
[ "1", "2", "3", "4", "5", "10", "11", "12", "13", "14", "15", "20", "21", "22", "27", "28", "29", "34", "35", "40", "41", "42", "43", "48", "49", "50", "51", "56", "57", "66", "67", "68", "69", "70", "75", "80", "81", "82", "83", "88", "89", "98", "99", "100", "109", "110", "111", "116", "117", "118", "119", "120", "121", "126", "127", "132", "133", "134", "135", "148", "149", "150", "155", "156", "157", "166", "167", "168", "169", "174", "175", "184", "185", "186", "191", "192", "197", "202", "203", "208" ]
[ "nonn" ]
24
1
2
[ "A000982", "A132188", "A362931", "A362932", "A362937" ]
null
N. J. A. Sloane, Aug 28 2023
2024-10-13T07:06:09
oeisdata/seq/A362/A362931.seq
33e364b5cc20712a4cbbed073313dc8d
A362932
a(n) = A132188(n) - A362931(n).
[ "0", "0", "0", "2", "2", "-2", "-2", "0", "4", "4", "4", "2", "2", "2", "-2", "4", "4", "4", "4", "2", "2", "2", "2", "0", "8", "8", "12", "10", "10", "2", "2", "8", "8", "8", "4", "10", "10", "10", "10", "8", "8", "0", "0", "2", "-2", "-2", "-2", "0", "12", "20", "20", "22", "22", "22", "22", "20", "20", "20", "20", "10", "10", "10", "10", "24", "24", "16", "16", "18", "18", "14", "14", "16", "16", "16", "20", "22", "18", "14", "14", "16" ]
[ "sign", "look" ]
18
1
4
[ "A132188", "A362931", "A362932" ]
null
N. J. A. Sloane, Aug 28 2023
2023-08-29T09:48:44
oeisdata/seq/A362/A362932.seq
3239f13c0b42311dab42223ad1e76d10
A362933
a(n) = (A132188(n) - A362931(n))/2.
[ "0", "0", "0", "1", "1", "-1", "-1", "0", "2", "2", "2", "1", "1", "1", "-1", "2", "2", "2", "2", "1", "1", "1", "1", "0", "4", "4", "6", "5", "5", "1", "1", "4", "4", "4", "2", "5", "5", "5", "5", "4", "4", "0", "0", "1", "-1", "-1", "-1", "0", "6", "10", "10", "11", "11", "11", "11", "10", "10", "10", "10", "5", "5", "5", "5", "12", "12", "8", "8", "9", "9", "7", "7", "8", "8", "8", "10", "11", "9", "7", "7", "8" ]
[ "sign", "look" ]
23
1
9
[ "A132188", "A362931", "A362932", "A362933" ]
null
N. J. A. Sloane, Aug 28 2023
2023-08-29T10:11:40
oeisdata/seq/A362/A362933.seq
ec09533ea92df8054619b18f1bdd9858
A362934
a(n) = A000982(n) - A132188(n).
[ "0", "0", "2", "2", "6", "10", "16", "20", "24", "32", "42", "50", "62", "74", "88", "96", "112", "124", "142", "158", "178", "198", "220", "240", "256", "280", "302", "326", "354", "382", "412", "436", "468", "500", "534", "558", "594", "630", "668", "704", "744", "784", "826", "866", "906", "950", "996", "1036", "1072", "1112", "1162", "1210", "1262", "1310", "1364", "1416", "1472", "1528", "1586", "1642", "1702", "1762" ]
[ "nonn" ]
11
1
3
[ "A000982", "A132188", "A362931", "A362934", "A932937" ]
null
N. J. A. Sloane, Aug 28 2023
2023-08-29T10:11:51
oeisdata/seq/A362/A362934.seq
6f1264fbb87c2b3fa1be00f16b122e9d
A362935
a(n) = (A000982(n) - A132188(n))/2.
[ "0", "0", "1", "1", "3", "5", "8", "10", "12", "16", "21", "25", "31", "37", "44", "48", "56", "62", "71", "79", "89", "99", "110", "120", "128", "140", "151", "163", "177", "191", "206", "218", "234", "250", "267", "279", "297", "315", "334", "352", "372", "392", "413", "433", "453", "475", "498", "518", "536", "556", "581", "605", "631", "655", "682", "708", "736", "764", "793", "821", "851", "881", "910", "934", "966", "998" ]
[ "nonn" ]
11
1
5
[ "A000982", "A132188", "A362931", "A362935", "A932937" ]
null
N. J. A. Sloane, Aug 28 2023
2023-08-29T10:12:04
oeisdata/seq/A362/A362935.seq
91e4ba5f9fe943a8f4f3af972bb9a28e
A362936
a(n) = A000982(n) - A362931(n).
[ "0", "0", "2", "4", "8", "8", "14", "20", "28", "36", "46", "52", "64", "76", "86", "100", "116", "128", "146", "160", "180", "200", "222", "240", "264", "288", "314", "336", "364", "384", "414", "444", "476", "508", "538", "568", "604", "640", "678", "712", "752", "784", "826", "868", "904", "948", "994", "1036", "1084", "1132", "1182", "1232", "1284", "1332", "1386", "1436", "1492", "1548", "1606", "1652", "1712" ]
[ "nonn" ]
13
1
3
[ "A000982", "A132188", "A362931", "A362936", "A932937" ]
null
N. J. A. Sloane, Aug 28 2023
2023-08-29T10:11:13
oeisdata/seq/A362/A362936.seq
7e509e3948870bebcdb28ed56f1f1629
A362937
a(n) = (A000982(n) - A362931(n))/2.
[ "0", "0", "1", "2", "4", "4", "7", "10", "14", "18", "23", "26", "32", "38", "43", "50", "58", "64", "73", "80", "90", "100", "111", "120", "132", "144", "157", "168", "182", "192", "207", "222", "238", "254", "269", "284", "302", "320", "339", "356", "376", "392", "413", "434", "452", "474", "497", "518", "542", "566", "591", "616", "642", "666", "693", "718", "746", "774", "803", "826", "856", "886", "915", "946", "978" ]
[ "nonn" ]
13
1
4
[ "A000982", "A362931", "A362936", "A362937" ]
null
N. J. A. Sloane, Aug 28 2023
2023-08-29T10:12:16
oeisdata/seq/A362/A362937.seq
fef3372db9c1a05b0745a4d27b6ad20f
A362938
a(n) = minimum number of pieces needed to dissect a regular n-sided polygon into a monotile, i.e. a polygonal tile which tiles the plane (conjectured).
[ "1", "1", "2", "1", "3", "2", "3", "2", "4", "3", "4", "3", "5", "4", "6" ]
[ "nonn", "more", "hard" ]
165
3
3
[ "A110312", "A362938", "A362939" ]
null
N. J. A. Sloane, Aug 29 2023
2023-10-11T00:24:17
oeisdata/seq/A362/A362938.seq
7f52b46c9c21ce557e6ce1fe3905b7f5
A362939
a(n) = minimum number of pieces needed to dissect a regular n-sided polygon into a rectangle (conjectured).
[ "2", "1", "4", "3", "5", "4", "7", "4", "9", "5", "10", "7", "10", "9" ]
[ "nonn", "more", "hard" ]
39
3
1
[ "A110312", "A362938", "A362939" ]
null
N. J. A. Sloane, Aug 31 2023
2023-09-27T15:00:58
oeisdata/seq/A362/A362939.seq
c2a6fce4f8d342f5b67d4344b7cf530b
A362940
Consider the Collatz trajectory from n to 1, assuming the Collatz conjecture is true. Then a(n) = number of terms in the trajectory that are greater than 1 and congruent to 1 mod 3. If n never reaches 1, set a(n) = -1.
[ "0", "0", "3", "1", "2", "3", "9", "1", "10", "3", "7", "3", "5", "9", "8", "2", "6", "10", "11", "3", "3", "8", "7", "3", "13", "5", "61", "10", "9", "8", "59", "2", "14", "7", "6", "10", "12", "11", "18", "4", "60", "3", "17", "8", "8", "8", "57", "3", "14", "13", "12", "6", "5", "61", "62", "10", "18", "10", "17", "8", "10", "59", "58", "3", "15", "14", "15", "7", "7", "7", "56", "10", "64", "12", "7", "12" ]
[ "nonn", "changed" ]
12
1
3
[ "A006577", "A008908", "A362940" ]
null
N. J. A. Sloane, Sep 11 2023, suggested by a sequence submitted by Emanuel Landeholm on Sep 10 2023 but later withdrawn, which had a somewhat different definition and contained errors
2025-07-09T05:02:24
oeisdata/seq/A362/A362940.seq
563ae9eb1c569ae7e6a890ad26cf7633
A362941
Numbers of the form (p+1)*(p+3) where (p,p+2) is a twin prime pair (cf. A001359).
[ "24", "48", "168", "360", "960", "1848", "3720", "5328", "10608", "11880", "19320", "22800", "32760", "37248", "39600", "52440", "58080", "73440", "80088", "97968", "121800", "177240", "187488", "214368", "273528", "326040", "361200", "383160", "413448", "436920", "657720", "677328", "687240", "737880", "779688", "1042440", "1067088", "1104600" ]
[ "nonn", "changed" ]
15
1
1
[ "A001359", "A108604", "A362941" ]
null
N. J. A. Sloane, Sep 10 2023, following a suggestion from Jean-Claude Babois
2025-07-09T05:02:31
oeisdata/seq/A362/A362941.seq
d3218d38ee99afafb6dcac1c1f40d6ac
A362942
Partial sums of A229037.
[ "1", "2", "4", "5", "6", "8", "10", "14", "18", "19", "20", "22", "23", "24", "26", "28", "32", "36", "38", "42", "46", "51", "56", "64", "69", "74", "83", "84", "85", "87", "88", "89", "91", "93", "97", "101", "102", "103", "105", "106", "107", "109", "111", "115", "119", "121", "125", "129", "134", "139", "147", "152", "157", "166", "175", "179", "183", "188", "193" ]
[ "nonn" ]
25
1
2
[ "A003002", "A229037", "A362942" ]
null
N. J. A. Sloane, Sep 12 2023
2023-09-27T15:08:02
oeisdata/seq/A362/A362942.seq
120b54948bb4d52b4590babc5550887d
A362943
Irregular triangular array read by rows. T(n,k) is the number of n X n Boolean relation matrices whose row span is k, n >= 0, 1 <= k <= 2^n.
[ "1", "1", "1", "1", "9", "4", "2", "1", "49", "144", "198", "78", "36", "0", "6", "1", "225", "2500", "9650", "15864", "17640", "8784", "6936", "2304", "1320", "0", "288", "0", "0", "0", "24" ]
[ "nonn", "tabf", "more" ]
20
0
5
[ "A002416", "A060867", "A362943" ]
null
Geoffrey Critzer, May 09 2023
2023-05-11T03:22:09
oeisdata/seq/A362/A362943.seq
7bf417ca3729f67a63160135094e32f9
A362944
Number of set partitions of [2n] with n circular connectors.
[ "1", "0", "8", "61", "1339", "27497", "700526", "20738540", "701018049", "26600152925", "1118837321664", "51638294897821", "2593507095707555", "140767051300283971", "8208477680892328056", "511665532350037672814", "33945069368611365210831", "2387678179967017695888746", "177467827693197791991904437" ]
[ "nonn" ]
17
0
3
[ "A185983", "A362944" ]
null
Alois P. Heinz, May 09 2023
2023-05-09T19:42:11
oeisdata/seq/A362/A362944.seq
aa63237ee56fa9f57f3b2b0a6eb66505
A362945
Numbers k such that k + the sum of the fifth powers of its digits is again a fifth power.
[ "0", "210", "66374", "76933", "294137", "722571", "741300", "1023716", "2412593", "3959235", "4022940", "5090402", "6351886", "7821198", "9653864", "11808061", "11814811", "20427955", "24190287", "24239133", "24245187", "33518020", "33532714", "33536551", "39060306", "52476271", "52480534", "69255266", "69265142", "79091461", "89980491", "90147222" ]
[ "nonn", "base" ]
9
0
2
[ "A000584", "A055014", "A362945", "A362953", "A362954" ]
null
M. F. Hasler, Jun 15 2023
2025-06-27T21:42:25
oeisdata/seq/A362/A362945.seq
34680cd15692510a75187af291fbf59c
A362946
Positive integers that cannot be expressed as 1^e_1 + 2^e_2 + 3^e_3 ... + k^e_k with each exponent positive.
[ "2", "4", "7", "11", "13", "19", "25", "31" ]
[ "nonn", "hard" ]
20
1
1
[ "A000217", "A000330", "A000537", "A000538", "A000539", "A362946" ]
null
Robert C. Lyons, Jul 05 2023
2023-07-06T09:48:48
oeisdata/seq/A362/A362946.seq
44406bfa4d1e348e6ff35956fd2a824f
A362947
a(0) = 0, a(1) = 0; for n > 1, a(n) is the number of pairs of consecutive terms whose product has same value as a(n-2) * a(n-1).
[ "0", "0", "1", "2", "1", "2", "3", "1", "1", "1", "2", "4", "1", "1", "3", "2", "2", "2", "3", "3", "1", "3", "4", "1", "4", "5", "1", "1", "4", "6", "1", "4", "7", "1", "1", "5", "2", "1", "5", "3", "1", "5", "4", "2", "2", "8", "1", "3", "6", "1", "5", "5", "1", "6", "6", "1", "7", "2", "1", "6", "8", "1", "4", "9", "2", "2", "10", "3", "1", "7", "3", "1", "8", "5", "1", "7", "4", "2", "6", "2", "3", "9", "1", "2", "7", "2", "3", "10", "2", "4", "7", "3", "2", "11", "1", "1", "6", "12" ]
[ "nonn" ]
14
0
4
[ "A342585", "A347062", "A362947", "A364027", "A364036" ]
null
Scott R. Shannon, Jul 05 2023
2023-07-06T08:55:52
oeisdata/seq/A362/A362947.seq
ff0de5b2866b2ffa45a86de3dec7f678
A362948
Numbers whose sum of (distinct) prime divisors (A008472) equals 5.
[ "5", "6", "12", "18", "24", "25", "36", "48", "54", "72", "96", "108", "125", "144", "162", "192", "216", "288", "324", "384", "432", "486", "576", "625", "648", "768", "864", "972", "1152", "1296", "1458", "1536", "1728", "1944", "2304", "2592", "2916", "3072", "3125", "3456", "3888", "4374", "4608", "5184", "5832", "6144", "6912", "7776", "8748", "9216", "10368", "11664", "12288" ]
[ "nonn", "easy" ]
12
1
1
[ "A000351", "A008472", "A033845", "A362948" ]
null
M. F. Hasler, Jul 20 2023
2023-07-27T15:21:49
oeisdata/seq/A362/A362948.seq
b823641552033aea02f85587fc6c0436
A362949
Number of nonzero terms in the partial fraction decomposition of Leibniz's sum Sum_{k=1..n} (-1)^k/(1-2k).
[ "0", "1", "2", "3", "4", "4", "5", "6", "7", "8", "9", "9", "10", "11", "12", "13", "14", "13", "14", "15", "14", "15", "16", "15", "16", "17", "17", "18", "19", "19", "20", "21", "21", "21", "22", "21", "22", "23", "24", "23", "24", "24", "25", "25", "24", "25", "27", "27", "27", "28", "28", "29", "30", "30", "31", "32", "31", "32", "32", "33", "33", "34", "35", "35", "36" ]
[ "nonn" ]
23
0
3
null
null
M. F. Hasler, Jun 16 2023
2023-07-25T22:41:49
oeisdata/seq/A362/A362949.seq
36d329997fb80e199660e6143539f765
A362950
Bitmaps of king + rook vs. king checkmate patterns on a standard 8 X 8 board.
[ "65541", "65541", "65545", "65553", "65569", "65601", "65665", "66561", "131077", "131081", "131082", "131089", "131090", "131105", "131106", "131137", "131138", "131201", "131202", "262149", "262164", "262180", "262212", "262276", "327681", "524297", "524298", "524328", "524360", "524424", "1048593", "1048594" ]
[ "nonn", "fini", "full" ]
33
1
1
[ "A000120", "A007088", "A014311", "A362950" ]
null
M. F. Hasler, Jun 13 2023
2023-08-02T14:00:09
oeisdata/seq/A362/A362950.seq
0daa001e8d85289e9042fdc78ef4c201
A362951
a(n) is the Hamming distance between the binary expansions of n and phi(n) where phi is the Euler totient function (A000010).
[ "0", "2", "1", "2", "1", "1", "1", "2", "4", "3", "1", "1", "1", "1", "3", "2", "1", "2", "1", "3", "3", "3", "1", "1", "3", "3", "2", "1", "1", "3", "1", "2", "4", "3", "5", "2", "1", "3", "6", "3", "1", "3", "1", "3", "4", "3", "1", "1", "4", "3", "3", "3", "1", "2", "5", "1", "4", "3", "1", "3", "1", "1", "4", "2", "4", "4", "1", "3", "4", "5", "1", "2", "1", "5", "4", "3", "4", "4", "1", "3", "5", "5", "1", "3", "3", "5", "6" ]
[ "nonn", "base", "less" ]
47
1
2
[ "A000010", "A000120", "A065091", "A101080", "A169814", "A362951" ]
null
Darío Clavijo, Jul 05 2023
2024-02-20T07:44:44
oeisdata/seq/A362/A362951.seq
cb7ea3d355a2146d5a03098401c989d5
A362952
Sum of divisors of 5*n-1 of form 5*k+2.
[ "2", "0", "9", "0", "14", "0", "19", "0", "24", "7", "29", "0", "34", "0", "39", "0", "63", "0", "49", "0", "54", "0", "59", "24", "64", "0", "69", "0", "86", "0", "108", "0", "84", "0", "89", "0", "94", "34", "99", "0", "133", "0", "109", "0", "153", "0", "119", "0", "124", "0", "129", "44", "168", "0", "139", "0", "144", "17", "198", "0", "154", "0", "159", "0", "203", "54", "169", "0", "174", "0", "179", "0", "243", "0", "228", "0", "238", "0", "199", "64", "204" ]
[ "nonn" ]
15
1
1
[ "A284280", "A359287", "A362952", "A363025", "A363026", "A363027", "A363028" ]
null
Seiichi Manyama, Jul 06 2023
2023-07-06T07:28:45
oeisdata/seq/A362/A362952.seq
2d62fdb5c48d62b10edc300701506532
A362953
Numbers N such that N + the sum of the cubes of its digits is again a third power.
[ "0", "34", "352", "540", "1167", "1942", "2176", "3312", "4093", "5454", "8019", "9380", "12025", "12130", "13068", "13158", "15344", "15991", "16279", "16675", "21149", "22699", "22789", "30988", "32257", "32365", "35238", "37883", "37955", "41866", "45549", "54523", "57906", "58530", "62579", "72588", "83692", "83782", "89604", "102952" ]
[ "nonn", "base" ]
37
0
2
[ "A000578", "A055012", "A362953", "A362954" ]
null
Will Gosnell and M. F. Hasler, May 09 2023
2023-06-02T10:20:58
oeisdata/seq/A362/A362953.seq
975adfaab76b54d4876864ad174c824f
A362954
Numbers k such that k + the sum of the fourth powers of its digits is again a fourth power.
[ "0", "6047", "7518", "8127", "12207", "25247", "50000", "71966", "77326", "89582", "156156", "376189", "384624", "384640", "599611", "611356", "700158", "794139", "796715", "800558", "1172829", "1329051", "1329324", "1329340", "1488080", "1492525", "1862190", "2546894", "2547885", "5295852", "5302286", "5755548", "6244080", "6246510", "7291980", "7869294" ]
[ "nonn", "base" ]
16
0
2
[ "A000583", "A055013", "A362953", "A362954" ]
null
Will Gosnell and M. F. Hasler, May 09 2023
2023-08-02T14:00:33
oeisdata/seq/A362/A362954.seq
95f4050a9c84847bc72b3c79b6979811
A362955
a(n) is the x-coordinate of the n-th point in a square spiral mapped to a square grid rotated by Pi/4 using the distance-limited strip bijection described in A307110.
[ "0", "1", "0", "-1", "-2", "-1", "0", "1", "2", "2", "1", "1", "0", "0", "-1", "-2", "-3", "-2", "-1", "-1", "0", "0", "1", "2", "3", "4", "3", "2", "2", "1", "0", "-1", "-1", "-2", "-3", "-3", "-4", "-4", "-3", "-2", "-2", "-1", "0", "1", "1", "2", "3", "3", "4", "5", "4", "3", "3", "2", "1", "0", "0", "-1", "-2", "-2", "-3", "-4", "-4", "-5", "-5", "-5", "-4", "-3", "-3", "-2", "-1", "0", "0", "1", "2", "2", "3", "4", "4", "5", "5", "6" ]
[ "sign" ]
16
0
5
[ "A174344", "A274923", "A307110", "A307731", "A362955", "A362956" ]
null
Hugo Pfoertner, May 10 2023
2023-05-10T09:46:42
oeisdata/seq/A362/A362955.seq
6037f9197ccbbf0ba5987a04770653a7
A362956
a(n) is the y-coordinate of the n-th point in a square spiral mapped to a square grid rotated by Pi/4 using the distance-limited strip bijection described in A307110.
[ "0", "0", "1", "1", "0", "0", "-1", "-1", "0", "1", "1", "2", "3", "2", "2", "1", "0", "-1", "-1", "-2", "-3", "-2", "-2", "-1", "0", "1", "1", "2", "3", "3", "4", "4", "3", "2", "2", "1", "0", "-1", "-1", "-2", "-3", "-3", "-4", "-4", "-3", "-2", "-2", "-1", "0", "1", "2", "2", "3", "4", "4", "5", "6", "5", "4", "3", "3", "2", "1", "1", "0", "-1", "-2", "-2", "-3", "-4", "-4", "-5", "-6", "-5", "-4", "-3", "-3", "-2", "-1", "-1", "0", "0" ]
[ "sign" ]
10
0
12
[ "A174344", "A274923", "A307110", "A307731", "A362955", "A362956" ]
null
Hugo Pfoertner, May 10 2023
2023-05-10T09:47:33
oeisdata/seq/A362/A362956.seq
9a9a71d3b5d92f6ac9d097ffa9a92b90
A362957
a(n) is the least prime p such that the number of distinct prime factors of p^n + 1 sets a new record.
[ "2", "3", "5", "43", "17", "47", "151", "1697", "59", "2153", "521", "13183", "30089", "20753", "3769" ]
[ "nonn", "hard", "more" ]
8
1
1
[ "A001221", "A115973", "A125137", "A280005", "A362957" ]
null
Hugo Pfoertner, Jun 11 2023
2023-06-13T15:39:48
oeisdata/seq/A362/A362957.seq
6895178cb93392b45defafd5b83c841f
A362958
a(n) is the number of primes in a Collatz orbit started at A078373(n).
[ "1", "3", "6", "7", "25", "26", "28", "29", "30", "32", "36", "37", "43", "44", "48", "50", "51", "52", "53", "55", "59", "61", "62", "67", "70", "73", "74", "75", "77", "78", "79", "80", "81", "82", "84", "85", "86", "87", "90", "92" ]
[ "nonn", "more" ]
4
1
2
[ "A055509", "A078350", "A362958" ]
null
Hugo Pfoertner, May 19 2023
2023-05-19T14:19:22
oeisdata/seq/A362/A362958.seq
6415477382f3f3217c5f240672532dc4
A362959
Numbers k such that the Collatz orbit that begins with k does not contain an odd prime afterwards.
[ "4", "5", "8", "16", "21", "32", "42", "64", "84", "85", "113", "128", "168", "170", "227", "256", "336", "340", "341", "453", "512", "672", "680", "682", "906", "909", "1024", "1344", "1360", "1364", "1365", "1812", "1813", "1818", "2048", "2417", "2688", "2720", "2728", "2730", "3624", "3626", "3636", "3637", "4096", "5376", "5440", "5456", "5460", "5461", "7248" ]
[ "nonn" ]
15
1
1
[ "A000079", "A006370", "A006577", "A196871", "A362959" ]
null
Hugo Pfoertner, May 18 2023
2023-05-19T13:20:17
oeisdata/seq/A362/A362959.seq
ec4772b35ed8403d5b272875fe946083
A362960
Length of longest Roman numeral representation of a number <= n.
[ "1", "2", "3", "3", "3", "3", "3", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8" ]
[ "nonn", "base", "easy" ]
26
1
2
[ "A006968", "A362960" ]
null
Leyang Zou, Aug 05 2023
2023-09-06T21:12:17
oeisdata/seq/A362/A362960.seq
268147c2de5f2b89366f4fdd019f0985
A362961
a(n) = Sum_{b=0..floor(sqrt(n)), n-b^2 is square} b.
[ "1", "1", "0", "2", "3", "0", "0", "2", "3", "4", "0", "0", "5", "0", "0", "4", "5", "3", "0", "6", "0", "0", "0", "0", "12", "6", "0", "0", "7", "0", "0", "4", "0", "8", "0", "6", "7", "0", "0", "8", "9", "0", "0", "0", "9", "0", "0", "0", "7", "13", "0", "10", "9", "0", "0", "0", "0", "10", "0", "0", "11", "0", "0", "8", "20", "0", "0", "10", "0", "0", "0", "6", "11", "12", "0", "0", "0", "0", "0", "12", "9", "10", "0" ]
[ "nonn", "look" ]
35
1
4
[ "A000925", "A001481", "A022544", "A143574", "A362961" ]
null
Darío Clavijo, May 10 2023
2023-05-16T12:53:27
oeisdata/seq/A362/A362961.seq
94a76035c5438bfa466e9fa8e728639a
A362962
Lexicographically earliest sequence of distinct positive terms such that if a(n) jumps over a(n) positions towards the right (landing on the integer k), the sum a(n) + k is always prime.
[ "1", "2", "4", "5", "3", "6", "7", "9", "10", "8", "11", "12", "13", "14", "16", "17", "15", "20", "21", "19", "22", "23", "18", "24", "25", "26", "28", "29", "27", "30", "31", "37", "32", "36", "33", "34", "35", "38", "39", "40", "46", "41", "42", "45", "43", "44", "47", "48", "49", "50", "54", "51", "53", "55", "52", "61", "56", "60", "57", "58", "59", "62", "66", "63", "64", "65", "67", "68" ]
[ "nonn" ]
20
1
2
[ "A182115", "A230086", "A362962" ]
null
Eric Angelini, May 10 2023
2023-05-20T14:47:24
oeisdata/seq/A362/A362962.seq
45c090f6129127eb2e0990b9bf5cdca3
A362963
Number of semimagic quads squares that can be formed using cards from Quads-2^n deck, where the first row and column are fixed.
[ "112", "45280", "4023232", "136941952", "3099135232", "58520273920", "1015268864512", "16907404529152", "275952876324352", "4459246445032960", "71702061084923392", "1150074407046026752", "18423955949551785472", "294965554795552806400", "4720907498205382415872", "75546191122161343370752" ]
[ "nonn", "easy" ]
20
4
1
[ "A361495", "A361613", "A362874", "A362963", "A362964" ]
null
Tanya Khovanova and MIT PRIMES STEP senior group, May 10 2023
2023-07-18T07:36:11
oeisdata/seq/A362/A362963.seq
93442ca67e96c8f5821a214d796c2a80
A362964
Number of semimagic quad squares that can be formed using cards from Quads-2^n deck.
[ "36126720", "905542041600", "3379298591047680", "4173723561555394560", "3211490275093527920640", "1999224826411677961420800", "1126422803027648324787240960", "604702030645626380104520171520", "316988224809023889673442568437760" ]
[ "nonn" ]
23
4
1
[ "A361495", "A361613", "A362874", "A362963", "A362964" ]
null
Tanya Khovanova and MIT PRIMES STEP senior group, May 10 2023
2023-08-09T18:19:36
oeisdata/seq/A362/A362964.seq
a24557e54148862d8788841a758b3a16
A362965
Number of primes <= the n-th prime power.
[ "1", "2", "2", "3", "4", "4", "4", "5", "6", "6", "7", "8", "9", "9", "9", "10", "11", "11", "12", "13", "14", "15", "15", "16", "17", "18", "18", "19", "20", "21", "22", "22", "23", "24", "25", "26", "27", "28", "29", "30", "30", "30", "31", "31", "32", "33", "34", "35", "36", "37", "38", "39", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "53", "54", "54", "55", "56", "57", "58", "59", "60" ]
[ "nonn" ]
34
1
2
[ "A000720", "A000961", "A246655", "A362965", "A366833" ]
null
Max Alekseyev, Jun 03 2023
2024-11-02T09:11:26
oeisdata/seq/A362/A362965.seq
ce2d92ec0fa9a8a52f426cfbbe2b29c8
A362966
Numbers k such that A007908(k) == 1 (mod k).
[ "1", "121487", "293957", "13449179", "549999887" ]
[ "nonn", "base", "hard", "more" ]
17
1
2
[ "A007908", "A029455", "A029479", "A110740", "A362966" ]
null
Max Alekseyev, Jun 06 2023
2024-10-12T09:02:14
oeisdata/seq/A362/A362966.seq
5987e102274edd673f46177bfd2821e2
A362967
Number of nondecreasing partitions of n^2 into n parts from the intervals [1,n], [2,n+1], ..., [n,2n-1], respectively.
[ "1", "1", "2", "5", "17", "66", "294", "1393", "6965", "36111", "192850", "1053894", "5871306", "33234990", "190704140", "1107086841", "6492325565", "38412063755", "229052915708", "1375396927729", "8310509070747", "50496841617102", "308394124109340", "1892137615326526", "11658149626059204", "72108088307308032", "447590893613564372" ]
[ "nonn" ]
12
0
3
[ "A019589", "A039744", "A077045", "A362967" ]
null
Max Alekseyev, Jun 16 2023
2023-06-18T13:36:26
oeisdata/seq/A362/A362967.seq
47c601ed3796ecfd4f18fb4be83846a0
A362968
Number of integral points in 2 * permutohedron of order n.
[ "1", "3", "19", "201", "3081", "62683", "1598955", "49180113", "1773405649", "73410669171", "3432267261699", "178922825114905", "10291053760222041", "647436905815864011", "44229766376059342171", "3260749830852693615777", "258039101519624535653025" ]
[ "nonn" ]
13
1
2
[ "A007747", "A138464", "A175176", "A362967", "A362968" ]
null
Max Alekseyev, Jun 17 2023
2023-06-22T06:04:36
oeisdata/seq/A362/A362968.seq
9c6d58405310a55d10959c2a3ece795a
A362969
Nonunitary near-perfect numbers: k such that nusigma(k) = k + d where d is a nonunitary divisor of k.
[ "48", "80", "96", "160", "224", "352", "416", "480", "896", "1472", "1476", "1856", "2688", "3968", "6016", "7552", "7808", "8550", "8700", "10332", "17010", "20300", "22496", "36448", "44384", "54944", "63488", "65024", "71264", "73710", "97300", "97792", "114176", "122368", "128512", "310976", "392192", "490496", "515072", "521216", "549990" ]
[ "nonn" ]
45
1
1
[ "A048146", "A181595", "A362969" ]
null
Jenaro Tomaszewski, May 10 2023
2023-05-20T04:35:51
oeisdata/seq/A362/A362969.seq
3a686caaed182ff0f0af6c2c9f95f1c6
A362970
Number of different "integer parts" of (possibly non-canonical) base-phi representations of n.
[ "1", "2", "2", "3", "3", "3", "3", "4", "5", "4", "5", "4", "4", "5", "6", "6", "5", "4", "5", "7", "6", "8", "7", "6", "6", "7", "8", "6", "7", "5", "5", "7", "9", "9", "8", "7", "8", "10", "8", "10", "8", "7", "8", "9", "9", "7", "5", "6", "9", "8", "11", "10", "9", "9", "11", "13", "10", "12", "9", "8", "10", "12", "12", "10", "8", "9", "12", "10", "13", "11", "9", "9", "10", "11", "8", "9", "6", "6", "9", "12" ]
[ "nonn", "base" ]
21
0
2
null
null
Jeffrey Shallit, May 11 2023
2023-05-12T08:58:25
oeisdata/seq/A362/A362970.seq
7dd08940ec1d434d3a878fbc86bdc2ce
A362971
Partials sums of the cubefull numbers (A036966).
[ "1", "9", "25", "52", "84", "148", "229", "354", "482", "698", "941", "1197", "1540", "1972", "2484", "3109", "3757", "4486", "5350", "6350", "7374", "8670", "10001", "11729", "13673", "15673", "17721", "19908", "22105", "24506", "27098", "29842", "32967", "36342", "39798", "43686", "47686", "51782", "56695", "61695", "66879", "72367", "78199" ]
[ "nonn" ]
17
1
2
[ "A036966", "A174172", "A362971", "A362974" ]
null
Amiram Eldar, May 13 2023
2023-05-13T06:17:31
oeisdata/seq/A362/A362971.seq
797d10930b506e99d7afafe9ea1c8cd4
A362972
Squarefree kernels of cubefull numbers (A036966).
[ "1", "2", "2", "3", "2", "2", "3", "5", "2", "6", "3", "2", "7", "6", "2", "5", "6", "3", "6", "10", "2", "6", "11", "6", "6", "10", "2", "3", "13", "7", "6", "14", "5", "15", "6", "6", "10", "2", "17", "10", "6", "14", "6", "3", "19", "6", "6", "10", "2", "21", "10", "15", "6", "22", "14", "6", "23", "6", "11", "6", "5", "10", "2", "7", "15", "6", "26", "14", "3", "10", "6", "22", "14", "6", "29", "10", "30", "6" ]
[ "nonn" ]
22
1
2
[ "A007947", "A036966", "A084371", "A362972", "A362974" ]
null
Amiram Eldar, May 13 2023
2025-03-27T05:43:33
oeisdata/seq/A362/A362972.seq
776c09cd9b7dc38a47872286bad2ead5
A362973
The number of cubefull numbers (A036966) not exceeding 10^n.
[ "1", "2", "7", "20", "51", "129", "307", "713", "1645", "3721", "8348", "18589", "41136", "90619", "198767", "434572", "947753", "2062437", "4480253", "9718457", "21055958", "45575049", "98566055", "213028539", "460160083", "993533517", "2144335391", "4626664451", "9980028172", "21523027285", "46408635232", "100053270534" ]
[ "nonn" ]
35
0
2
[ "A036966", "A070428", "A118896", "A362973", "A362974", "A362975", "A362976" ]
null
Amiram Eldar, May 11 2023
2024-01-01T11:56:28
oeisdata/seq/A362/A362973.seq
30e39738dab529beac2d071a3ec96c5e
A362974
Decimal expansion of Product_{p prime} (1 + 1/p^(4/3) + 1/p^(5/3)).
[ "4", "6", "5", "9", "2", "6", "6", "1", "2", "2", "5", "0", "0", "6", "5", "6", "9", "4", "1", "2", "7", "7", "4", "3", "1", "1", "0", "8", "9", "1", "3", "6", "2", "5", "8", "6", "2", "1", "3", "0", "5", "4", "3", "3", "6", "7", "2", "8", "3", "2", "5", "6", "5", "3", "8", "4", "7", "5", "7", "6", "9", "2", "4", "0", "1", "5", "3", "0", "3", "4", "1", "8", "0", "8", "6", "5", "7", "3", "5", "2", "3", "8", "7", "2", "1", "8", "0", "7", "7", "5", "8", "9", "0", "2", "6", "8", "4", "6", "2", "3", "4", "9", "0", "9", "7" ]
[ "nonn", "cons" ]
7
1
1
[ "A036966", "A051904", "A090699", "A244000", "A337736", "A362973", "A362974", "A362975", "A362976" ]
null
Amiram Eldar, May 11 2023
2025-03-24T08:54:39
oeisdata/seq/A362/A362974.seq
59af37b6b6d25dd5e281cb71076d6b81
A362975
Decimal expansion of zeta(3/4) * Product_{p prime} (1 + 1/p^(5/4) - 1/p^2 - 1/p^(9/4)) (negated).
[ "5", "8", "7", "2", "6", "1", "8", "8", "2", "0", "8", "1", "3", "8", "4", "2", "3", "9", "1", "0", "7", "4", "1", "3", "8", "1", "4", "2", "6", "6", "7", "8", "3", "5", "6", "1", "1", "4", "8", "6", "2", "6", "4", "3", "1", "1", "0", "8", "2", "9", "3", "5", "3", "5", "1", "7", "0", "7", "9", "8", "0", "4", "6", "6", "9", "0", "3", "9", "8", "2", "0", "5", "3", "5", "0", "1", "1", "2", "5", "3", "5", "6", "8", "6", "3", "3", "7", "5", "7", "9", "1", "7", "5", "1", "3", "0", "1", "2", "1", "3", "1", "6", "8", "4", "3" ]
[ "nonn", "cons" ]
5
1
1
[ "A036966", "A090699", "A244000", "A362973", "A362974", "A362975", "A362976" ]
null
Amiram Eldar, May 11 2023
2023-05-11T01:44:02
oeisdata/seq/A362/A362975.seq
104f8a20c2cd7ef46ab63b8548f79606
A362976
Decimal expansion of zeta(3/5) * zeta(4/5) * Product_{p prime} (1 - 1/p^(8/5) - 1/p^(9/5) - 1/p^2 + 1/p^(13/5) + 1/p^(14/5)).
[ "1", "6", "8", "2", "4", "4", "1", "5", "1", "0", "2", "3", "5", "9", "3", "2", "9", "3", "8", "9", "5", "6", "0", "0", "2", "0", "3", "4", "3", "1", "7", "7", "1", "2", "4", "5", "3", "3", "7", "2", "3", "3", "6", "2", "1", "3", "5", "7", "9", "9", "4", "9", "4", "3", "8", "5", "1", "5", "8", "3", "5", "4", "3", "9", "7", "4", "9", "6", "9", "8", "9", "7", "7", "6", "7", "6", "0", "1", "0", "6", "4", "7", "8", "5", "6", "2", "7", "7", "7", "7", "5", "4", "1", "9", "7", "6", "4", "3", "9", "5", "5", "6", "7", "5", "2" ]
[ "nonn", "cons" ]
5
1
2
[ "A036966", "A090699", "A244000", "A362973", "A362974", "A362975", "A362976" ]
null
Amiram Eldar, May 11 2023
2023-05-11T01:43:37
oeisdata/seq/A362/A362976.seq
15c5f5d320b2b42db427856a78c05dad
A362977
The x-coordinates of the even-ranked elements of the lexicographically earliest sequence of points satisfying staircase and no-three-in-a-line conditions (see comments).
[ "0", "1", "2", "5", "6", "3", "12", "13", "4", "15", "8", "27", "19", "11", "9", "32", "25", "16", "33", "35", "59", "30", "24", "7", "51", "45", "10", "18", "29", "26", "54", "58", "14", "53", "23", "34", "37", "49", "44", "60", "43", "31", "41", "66", "17", "72", "80", "81", "78", "88", "87", "46", "83", "22", "76", "79", "130", "97", "108", "111", "94", "119", "153", "89", "39", "112" ]
[ "nonn" ]
26
0
3
[ "A161680", "A362977", "A362978" ]
null
Luc Rousseau, May 11 2023
2025-01-06T21:46:04
oeisdata/seq/A362/A362977.seq
3840ce8eea61f42674e85bceee16f94f
A362978
The y-coordinates of the even-ranked elements of the lexicographically earliest sequence of points satisfying staircase and no-three-in-a-line conditions. Companion sequence of A362977.
[ "0", "1", "3", "2", "4", "7", "5", "8", "12", "11", "10", "6", "13", "23", "20", "14", "28", "21", "15", "24", "9", "35", "43", "38", "37", "52", "33", "45", "36", "32", "22", "44", "46", "59", "53", "54", "64", "19", "34", "27", "72", "70", "84", "74", "55", "49", "26", "50", "17", "31", "77", "56", "107", "85", "47", "60", "16", "62", "29", "25", "69", "41", "42", "106", "82", "61", "65" ]
[ "nonn" ]
7
0
3
[ "A362977", "A362978" ]
null
Luc Rousseau, May 11 2023
2023-07-07T06:16:35
oeisdata/seq/A362/A362978.seq
9c0afb5a440d1f0a044253007ee3f4b8
A362979
Square array, read by descending antidiagonals: row n lists the primes whose base-2 representation has exactly n ones, starting from n=3.
[ "7", "11", "23", "13", "29", "31", "19", "43", "47", "311" ]
[ "nonn", "base", "tabl", "more" ]
34
3
1
[ "A000040", "A014499", "A019434", "A061712", "A081091", "A095077", "A362979" ]
null
Clark Kimberling, May 11 2023
2024-01-19T08:13:57
oeisdata/seq/A362/A362979.seq
8403206dfd5499f89e6e0c0f63eb79d8
A362980
Numbers whose multiset of prime factors (with multiplicity) has different median from maximum.
[ "6", "10", "12", "14", "15", "20", "21", "22", "24", "26", "28", "30", "33", "34", "35", "36", "38", "39", "40", "42", "44", "45", "46", "48", "51", "52", "55", "56", "57", "58", "60", "62", "63", "65", "66", "68", "69", "70", "72", "74", "76", "77", "78", "80", "82", "84", "85", "86", "87", "88", "90", "91", "92", "93", "94", "95", "96", "99", "100", "102", "104", "105", "106", "110" ]
[ "nonn" ]
6
1
1
[ "A000040", "A001222", "A002865", "A027746", "A053263", "A056239", "A112798", "A171979", "A237821", "A237824", "A237984", "A240302", "A327473", "A327476", "A359908", "A362611", "A362613", "A362614", "A362615", "A362616", "A362619", "A362620", "A362621", "A362622", "A362980" ]
null
Gus Wiseman, May 12 2023
2023-05-12T12:43:45
oeisdata/seq/A362/A362980.seq
e1810646a243e0468a8e27080d926907
A362981
Heinz numbers of integer partitions such that 2*(least part) >= greatest part.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "11", "12", "13", "15", "16", "17", "18", "19", "21", "23", "24", "25", "27", "29", "31", "32", "35", "36", "37", "41", "43", "45", "47", "48", "49", "53", "54", "55", "59", "61", "63", "64", "65", "67", "71", "72", "73", "75", "77", "79", "81", "83", "89", "91", "96", "97", "101", "103", "105", "107", "108", "109", "113", "119", "121", "125" ]
[ "nonn" ]
6
1
2
[ "A001222", "A027746", "A053263", "A056239", "A081306", "A112798", "A171979", "A237820", "A237821", "A237824", "A327473", "A327476", "A362616", "A362619", "A362621", "A362622", "A362981", "A362982" ]
null
Gus Wiseman, May 14 2023
2023-05-14T09:39:47
oeisdata/seq/A362/A362981.seq
0291350164174e0a447e498b7ce8346d
A362982
Heinz numbers of partitions such that 2*(least part) < greatest part.
[ "10", "14", "20", "22", "26", "28", "30", "33", "34", "38", "39", "40", "42", "44", "46", "50", "51", "52", "56", "57", "58", "60", "62", "66", "68", "69", "70", "74", "76", "78", "80", "82", "84", "85", "86", "87", "88", "90", "92", "93", "94", "95", "98", "99", "100", "102", "104", "106", "110", "111", "112", "114", "115", "116", "117", "118", "120", "122", "123", "124", "126" ]
[ "nonn" ]
5
1
1
[ "A001222", "A027746", "A053263", "A056239", "A069900", "A081306", "A112798", "A171979", "A237820", "A237821", "A237824", "A327473", "A327476", "A362616", "A362619", "A362621", "A362622", "A362981", "A362982" ]
null
Gus Wiseman, May 14 2023
2023-05-14T09:39:43
oeisdata/seq/A362/A362982.seq
13c87c4cba92f1fcf2c82e7f7fc88d59
A362983
Number of prime factors of n (with multiplicity) that are greater than the least.
[ "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "1", "0", "0", "2", "0", "1", "1", "1", "0", "1", "0", "1", "0", "1", "0", "2", "0", "0", "1", "1", "1", "2", "0", "1", "1", "1", "0", "2", "0", "1", "1", "1", "0", "1", "0", "2", "1", "1", "0", "3", "1", "1", "1", "1", "0", "2", "0", "1", "1", "0", "1", "2", "0", "1", "1", "2", "0", "2", "0", "1", "2", "1", "1", "2", "0", "1", "0", "1", "0", "2", "1", "1", "1" ]
[ "nonn" ]
6
1
18
[ "A000961", "A001221", "A001222", "A024619", "A027746", "A047966", "A052126", "A053585", "A061395", "A064989", "A071178", "A072774", "A099856", "A105441", "A112798", "A124010", "A307517", "A325226", "A325230", "A362983", "A363128", "A363129", "A363131" ]
null
Gus Wiseman, May 18 2023
2023-05-18T23:26:26
oeisdata/seq/A362/A362983.seq
f8f1a54e17e5ce5209c56fba01dfdcf0
A362984
Decimal expansion of the asymptotic mean of the abundancy index of the powerful numbers (A001694).
[ "2", "1", "4", "9", "6", "8", "6", "9", "0", "3", "0", "1", "5", "2", "6", "7", "6", "5", "1", "2", "8", "2", "1", "9", "0", "4", "2", "1", "0", "5", "1", "0", "9", "4", "1", "6", "1", "4", "5", "9", "8", "7", "6", "5", "3", "2", "7", "5", "1", "0", "0", "9", "9", "9", "8", "7", "3", "2", "7", "3", "3", "4", "3", "7", "8", "9", "7", "6", "2", "7", "1", "7", "9", "4", "0", "3", "6", "4", "2", "3", "6", "5", "7", "4", "2", "7", "4", "2", "3", "7", "7", "1", "7", "0", "2", "4", "2", "2", "8", "9", "7", "3", "8", "6", "2" ]
[ "nonn", "cons" ]
7
1
1
[ "A000203", "A001694", "A013661", "A017665", "A017666", "A082020", "A111003", "A157292", "A157294", "A157296", "A180114", "A240976", "A245058", "A306633", "A362984", "A362985" ]
null
Amiram Eldar, May 12 2023
2023-05-12T04:22:34
oeisdata/seq/A362/A362984.seq
a9bbbda2ec75c3dd246823721a4de6ba
A362985
Decimal expansion of the asymptotic mean of the abundancy index of the cubefull numbers (A036966).
[ "2", "4", "8", "2", "1", "7", "9", "1", "9", "6", "4", "2", "2", "3", "5", "9", "5", "2", "5", "4", "6", "1", "6", "7", "6", "4", "3", "6", "7", "4", "6", "8", "7", "6", "9", "8", "5", "3", "6", "3", "6", "8", "9", "4", "0", "9", "7", "1", "9", "3", "0", "4", "6", "8", "3", "5", "4", "3", "6", "3", "9", "3", "2", "8", "1", "4", "4", "4", "2", "3", "3", "8", "8", "5", "7", "6", "7", "5", "0", "4", "6", "3", "4", "1", "1", "5", "0", "7", "3", "1", "0", "3", "9", "8", "0", "4", "4", "7", "4", "0", "3", "7", "3", "1", "0" ]
[ "nonn", "cons" ]
5
1
1
[ "A000203", "A013661", "A017665", "A017666", "A036966", "A082020", "A111003", "A157292", "A157294", "A157296", "A240976", "A245058", "A306633", "A362984", "A362985", "A362986" ]
null
Amiram Eldar, May 12 2023
2023-05-12T04:26:21
oeisdata/seq/A362/A362985.seq
455d1961fdf15652f15f088eee8f05ea
A362986
a(n) = A000203(A036966(n)), the sum of divisors of the n-th cubefull number A036966(n).
[ "1", "15", "31", "40", "63", "127", "121", "156", "255", "600", "364", "511", "400", "1240", "1023", "781", "1815", "1093", "2520", "2340", "2047", "3751", "1464", "5080", "5460", "4836", "4095", "3280", "2380", "2801", "7623", "6000", "3906", "6240", "10200", "11284", "9828", "8191", "5220", "11715", "15367", "12400", "16395", "9841", "7240", "20440" ]
[ "nonn" ]
19
1
2
[ "A000203", "A036966", "A180114", "A362974", "A362985", "A362986" ]
null
Amiram Eldar, May 12 2023
2024-09-21T14:48:30
oeisdata/seq/A362/A362986.seq
12b8f4fca4107d5595bc820d186e09e3
A362987
Lexicographically earliest sequence S of distinct positive terms such that the successive digits of S are the successive spreads of S' terms (see Comments for definition of "spread").
[ "10", "11", "12", "21", "23", "13", "20", "32", "24", "14", "34", "25", "31", "22", "30", "35", "42", "15", "43", "26", "36", "37", "46", "16", "41", "45", "53", "57", "47", "33", "52", "27", "40", "64", "54", "38", "48", "58", "68", "17", "63", "28", "69", "18", "51", "39", "56", "60", "59", "65", "62", "49", "50", "74", "61", "29", "73", "70", "85", "96", "72", "75", "79", "81", "84", "44", "71", "95", "83", "105", "104", "19" ]
[ "base", "nonn" ]
19
1
1
[ "A100787", "A362987" ]
null
Eric Angelini, May 12 2023
2023-05-20T14:46:29
oeisdata/seq/A362/A362987.seq
a0071b57e1df2f9b6324a6a417aecc99
A362988
a(n) = lcm({i, i = 1..n}) / Product_{2 <= p < n, p prime} p.
[ "1", "1", "2", "3", "2", "10", "2", "14", "4", "12", "12", "132", "12", "156", "12", "12", "24", "408", "24", "456", "24", "24", "24", "552", "24", "120", "120", "360", "360", "10440", "360", "11160", "720", "720", "720", "720", "720", "26640", "720", "720", "720", "29520", "720", "30960", "720", "720", "720", "33840", "720", "5040", "5040", "5040", "5040", "267120" ]
[ "nonn" ]
6
0
3
[ "A003418", "A034386", "A362988" ]
null
Peter Luschny, May 14 2023
2023-05-14T09:39:18
oeisdata/seq/A362/A362988.seq
43e06fd7f867fc80f1b879af67dc23c7
A362989
a(n) = lcm({i + 1, i = 0..n}) / Product_{d | n, d + 1 prime} d.
[ "1", "1", "1", "6", "2", "30", "10", "420", "84", "1260", "420", "13860", "132", "180180", "60060", "360360", "24024", "6126120", "291720", "116396280", "705432", "116396280", "38798760", "2677114440", "9806280", "13385572200", "13385572200", "40156716600", "2677114440", "1164544781400", "5041319400", "72201776446800" ]
[ "nonn" ]
4
0
4
[ "A003418", "A160014", "A362989" ]
null
Peter Luschny, May 14 2023
2023-05-14T09:39:14
oeisdata/seq/A362/A362989.seq
41e882c695accd421e9c42ffcdc752da
A362990
Row sums of A363154.
[ "1", "1", "3", "8", "70", "156", "2982", "19296", "216396", "917480", "47847580", "250815120", "18724750980", "116905717320", "788402337660", "11422960203648", "1503958432951464", "12400297557081840", "2060467159019459400", "19050402239258292000", "185663459342909159640", "1902329957427442126320" ]
[ "nonn" ]
3
0
3
[ "A173018", "A349203", "A362990", "A363154" ]
null
Peter Luschny, May 22 2023
2023-05-22T06:22:30
oeisdata/seq/A362/A362990.seq
de7098ff9c4d2f51218f889fa7dd9bca
A362991
Triangle read by rows. T(n, k) = lcm{1, 2, ..., n+1} * Sum_{j=0..n-k} (-1)^(n-k-j) * j! * Stirling2(n - k, j) / (j + k + 1).
[ "1", "1", "1", "1", "2", "2", "0", "2", "3", "3", "-2", "2", "9", "12", "12", "0", "-2", "3", "8", "10", "10", "10", "-10", "-9", "24", "50", "60", "60", "0", "20", "-30", "-8", "50", "90", "105", "105", "-84", "84", "18", "-96", "0", "150", "245", "280", "280", "0", "-84", "126", "-24", "-90", "18", "147", "224", "252", "252", "2100", "-2100", "126", "1344", "-600", "-870", "343", "1568", "2268", "2520", "2520" ]
[ "sign", "tabl" ]
22
0
5
[ "A002944", "A027642", "A051714", "A051715", "A164555", "A362991", "A362994" ]
null
Peter Luschny, May 16 2023
2023-08-09T08:01:59
oeisdata/seq/A362/A362991.seq
27be54ca8d209230a88152b5f20c05d5
A362992
a(n) = (n + 1)^(n - 1) * lcm{k + 1 : 0 <= k <= n}. Main diagonal of triangle A362995.
[ "1", "2", "18", "192", "7500", "77760", "7058940", "220200960", "12053081880", "252000000000", "65362309994520", "1716349336289280", "645822919595173320", "20430218263561666560", "701330854833984375000", "51933349175015422033920", "35071094208630625451626320", "1487906280482935955379978240" ]
[ "nonn" ]
13
0
2
[ "A000272", "A003418", "A362992", "A362995" ]
null
Peter Luschny, May 15 2023
2023-08-09T08:01:47
oeisdata/seq/A362/A362992.seq
fa0f4ef0236051432efaaaeae99925da
A362993
Row sums of A362995.
[ "1", "5", "139", "8920", "3140313", "386431752", "514497175965", "279843094350688", "309269596069652505", "148299194161602748000", "987531598214016848643771", "736658715557644007659575408", "8631341032315887149556551616665", "9247541236236479803404967113812944", "11617153578430950909883928682002963745" ]
[ "nonn" ]
4
0
2
[ "A362993", "A362995" ]
null
Peter Luschny, May 14 2023
2023-05-20T08:22:46
oeisdata/seq/A362/A362993.seq
e47e19936fd23108046cd11d7a606929
A362994
a(n) = lcm(1, 2, ..., n+1) * Bernoulli(n, 1). Alternating row sums of A362995 and A363154.
[ "1", "1", "1", "0", "-2", "0", "10", "0", "-84", "0", "2100", "0", "-91212", "0", "420420", "0", "-86894808", "0", "12796881240", "0", "-123176186952", "0", "33154044803880", "0", "-2317852458291480", "0", "114488177740536600", "0", "-63580025062953158760", "0", "43435207772044760997000", "0", "-2182849703429651931795120" ]
[ "sign" ]
20
0
5
[ "A003418", "A027642", "A164555", "A362991", "A362994", "A362995", "A363154" ]
null
Peter Luschny, May 14 2023
2023-08-09T08:02:08
oeisdata/seq/A362/A362994.seq
9858e6373ce2723a7bd5f60cb2814e71
A362995
Triangle read by rows. T(n, k) = [x^k] lcm({i + 1 : 0 <= i <= n}) * (Sum_{u=0..k} ( Sum_{j=0..u} x^j * binomial(u, j) * (j + 1)^n ) / (u + 1)).
[ "1", "3", "2", "11", "28", "18", "25", "184", "351", "192", "137", "2608", "11097", "16128", "7500", "147", "6816", "57591", "166912", "193750", "77760", "1089", "118464", "1865511", "9588736", "20843750", "20062080", "7058940", "2283", "567936", "16015401", "136921088", "495546875", "858003840", "704129265", "220200960" ]
[ "nonn", "tabl" ]
18
0
2
[ "A001008", "A362992", "A362993", "A362994", "A362995", "A362996", "A362997", "A363000" ]
null
Peter Luschny, May 14 2023
2025-01-15T06:10:15
oeisdata/seq/A362/A362995.seq
80dfb75d63504eb027ac874f2f076c8a
A362996
Triangle read by rows. T(n, k) = numerator([x^k] R(n, n, x)), where R(n, k, x) = Sum_{u=0..k} ( Sum_{j=0..u} x^j * binomial(u, j) * (j + 1)^n ) / (u + 1).
[ "1", "3", "1", "11", "14", "3", "25", "46", "117", "16", "137", "652", "3699", "1344", "125", "49", "568", "19197", "41728", "19375", "1296", "363", "9872", "621837", "2397184", "2084375", "334368", "16807", "761", "23664", "5338467", "17115136", "99109375", "7150032", "6705993", "262144" ]
[ "nonn", "tabl", "frac" ]
13
0
2
[ "A000272", "A001008", "A362995", "A362996", "A362997" ]
null
Peter Luschny, May 13 2023
2023-05-20T08:22:24
oeisdata/seq/A362/A362996.seq
d7f0e6636edd1e166bbd37e5389d6e29
A362997
Triangle read by rows. T(n, k) = denominator([x^k] R(n, n, x)), where R(n, k, x) = Sum_{u=0..k} ( Sum_{j=0..u} x^j * binomial(u, j) * (j + 1)^n ) / (u + 1).
[ "1", "2", "1", "6", "3", "1", "12", "3", "4", "1", "60", "15", "20", "5", "1", "20", "5", "20", "15", "6", "1", "140", "35", "140", "105", "42", "7", "1", "280", "35", "280", "105", "168", "7", "8", "1", "2520", "315", "280", "315", "504", "7", "72", "9", "1", "2520", "315", "280", "315", "504", "35", "360", "45", "10", "1", "27720", "3465", "3080", "3465", "5544", "385", "3960", "495", "110", "11", "1" ]
[ "nonn", "tabl", "frac" ]
13
0
2
[ "A002805", "A362995", "A362996", "A362997" ]
null
Peter Luschny, May 13 2023
2023-05-20T08:22:19
oeisdata/seq/A362/A362997.seq
e2b73d4232461c0606db3efc43b519d0
A362998
a(n) = Sum_{k=0..2*n} R(2*n, k, 1) where R(n, k, x) = Sum_{u=0..k} ( Sum_{j=0..u} x^j * binomial(u, j) * (j + 1)^n ) / (u + 1).
[ "1", "14", "867", "191476", "92323925", "78056422494", "102352057350319", "192403045957195112", "490874140662802917417", "1632516441577827373044370", "6861835036233587237791174211", "35570322051950868085847089286364", "222935341340851671535556256425205757", "1661810870170209385499116531813558149446" ]
[ "nonn" ]
5
0
2
[ "A362998", "A363000" ]
null
Peter Luschny, May 12 2023
2023-05-12T15:57:48
oeisdata/seq/A362/A362998.seq
0e5721a23a18ebc882f58c5c94712703
A362999
a(n) = denominator(R(2*n + 1, 2*n + 1, 1)) where R(n, k, x) = Sum_{u=0..k} ( Sum_{j=0..u} x^j * binomial(u, j) * (j + 1)^n ) / (u + 1).
[ "2", "3", "15", "105", "315", "3465", "45045", "9009", "153153", "14549535", "14549535", "19684665", "1673196525", "5019589575", "145568097675", "4512611027925", "4512611027925", "4512611027925", "166966608033225", "316824683175", "6845630929362225", "294362129962575675", "294362129962575675", "13835020108241056725" ]
[ "nonn", "frac" ]
9
0
1
[ "A362999", "A363000", "A363001" ]
null
Peter Luschny, May 12 2023
2023-05-12T15:57:38
oeisdata/seq/A362/A362999.seq
dcc15838a255a311cbffd64ee747258c
A363000
a(n) = numerator(R(n, n, 1)), where R are the rational polynomials R(n, k, x) = Sum_{u=0..k} ( Sum_{j=0..u} x^j * binomial(u, j) * (j + 1)^n ) / (u + 1).
[ "1", "5", "19", "188", "1249", "125744", "283517", "303923456", "138604561", "599865008128", "118159023973", "7078040993755136", "155792758736921", "146303841678548271104", "294014633772018349", "64670474732430319157248", "752324747622089633569", "3224753626003393505960919040", "2507759850059601711479669" ]
[ "nonn", "frac" ]
21
0
2
[ "A027611", "A027612", "A062709", "A362998", "A362999", "A363000", "A363001" ]
null
Peter Luschny, May 12 2023
2025-05-06T11:27:00
oeisdata/seq/A363/A363000.seq
97e576238185455563f01def778f2d56