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348
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score
int64
1
2.31k
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int64
-14,827
666,262,453B
offset_b
int64
0
635M
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1999-12-11 03:00:00
2025-04-28 00:58:08
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A361001
Triangle read by rows: T(n,k) is the number of tilings of an n X k rectangle by integer-sided rectangular pieces that cannot be rearranged to produce a different tiling of the rectangle (except rotations and reflections of the original tiling), 1 <= k <= n.
[ "1", "2", "4", "3", "7", "9", "4", "11", "18", "23", "4", "14", "22", "34", "41", "6", "23", "42", "72", "108" ]
[ "nonn", "tabl", "more" ]
7
1
2
[ "A000005", "A360629", "A360998", "A361001", "A361002", "A361003", "A361004", "A361005" ]
null
Pontus von Brömssen, Feb 28 2023
2023-03-02T06:22:18
oeisdata/seq/A361/A361001.seq
9d822d3eef2b1366664ab4d2a904a998
A361002
Number of tilings of an n X n square by integer-sided rectangular pieces that cannot be rearranged to produce a different tiling of the square (except rotations and reflections of the original tiling).
[ "1", "4", "9", "23", "41" ]
[ "nonn", "more" ]
6
1
2
[ "A360630", "A361001", "A361002" ]
null
Pontus von Brömssen, Feb 28 2023
2023-03-02T06:22:30
oeisdata/seq/A361/A361002.seq
71537e163751873e8dd3078f49dc6af3
A361003
a(n) = A000005(n) + floor((n-1)/2).
[ "1", "2", "3", "4", "4", "6", "5", "7", "7", "8", "7", "11", "8", "10", "11", "12", "10", "14", "11", "15", "14", "14", "13", "19", "15", "16", "17", "19", "16", "22", "17", "21", "20", "20", "21", "26", "20", "22", "23", "27", "22", "28", "23", "27", "28", "26", "25", "33", "27", "30", "29", "31", "28", "34", "31", "35", "32", "32", "31", "41", "32", "34", "37", "38", "36", "40", "35", "39" ]
[ "nonn" ]
6
1
2
[ "A000005", "A361001", "A361003" ]
null
Pontus von Brömssen, Feb 28 2023
2023-03-02T06:22:38
oeisdata/seq/A361/A361003.seq
33a57c93aad0eeed85323847dac710e0
A361004
Number of tilings of an n X 2 rectangle by integer-sided rectangular pieces that cannot be rearranged to produce a different tiling of the rectangle (except rotations and reflections of the original tiling).
[ "2", "4", "7", "11", "14", "23", "22", "32", "37", "42", "39", "69", "50", "64" ]
[ "nonn", "more" ]
7
1
1
[ "A360631", "A360999", "A361001", "A361004" ]
null
Pontus von Brömssen, Feb 28 2023
2023-03-02T06:23:00
oeisdata/seq/A361/A361004.seq
c0fdf8e49be0d7554bdb44569eeff690
A361005
Number of tilings of an n X 3 rectangle by integer-sided rectangular pieces that cannot be rearranged to produce a different tiling of the rectangle (except rotations and reflections of the original tiling).
[ "3", "7", "9", "18", "22", "42", "48", "86", "101" ]
[ "nonn", "more" ]
6
1
1
[ "A360632", "A361000", "A361001", "A361005" ]
null
Pontus von Brömssen, Feb 28 2023
2023-03-02T06:23:08
oeisdata/seq/A361/A361005.seq
a9902f9f012e466a608197dab9bb1481
A361006
Decimal expansion of conventional value of volt-90 (V_{90}).
[ "1", "0", "0", "0", "0", "0", "0", "1", "0", "6", "6", "6", "5", "1", "0", "7", "2", "5", "0", "5", "9", "0", "4", "4", "8", "9", "4", "2", "9", "7", "2", "1", "6", "4", "2", "0", "3", "9", "6", "2", "5", "4", "5", "1", "1", "8", "4", "8", "0", "3", "6", "3", "5", "0", "7", "7", "8", "5", "3", "7", "1", "9", "3", "4", "2", "1", "5", "8", "3", "7", "5", "2", "7", "9", "3", "6", "3", "8", "6", "0", "7", "0", "1", "5", "1", "6", "1" ]
[ "cons", "nonn", "easy" ]
11
-8
10
[ "A248508", "A361006" ]
null
Marco Ripà, Feb 28 2023
2023-04-23T22:30:57
oeisdata/seq/A361/A361006.seq
f4a2c0ae6fa6864888e01f02150e972d
A361007
a(n) = numerator of (zeta(2*n,1/4) + zeta(2*n,3/4))/Pi^(2*n) where zeta is the Hurwitz zeta function.
[ "0", "2", "8", "64", "2176", "31744", "2830336", "178946048", "30460116992", "839461371904", "232711080902656", "39611984424992768", "955693069653508096", "1975371841521663868928", "1124025625663103358205952", "369906947004953565463576576", "278846808228005417477465964544" ]
[ "nonn", "frac" ]
33
0
2
[ "A000364", "A036279", "A046982", "A173945", "A173947", "A173948", "A173949", "A173953", "A173954", "A173955", "A173982", "A173983", "A173984", "A173987", "A360945", "A360966", "A361007" ]
null
Artur Jasinski, Mar 15 2023
2023-06-11T12:04:21
oeisdata/seq/A361/A361007.seq
db6edb19efc712890da53ac50c83392e
A361008
G.f.: Product_{k >= 0} ((1 + x^(2*k+1)) / (1 - x^(2*k+1)))^k.
[ "1", "0", "0", "2", "0", "4", "2", "6", "8", "10", "20", "18", "42", "40", "78", "92", "140", "192", "258", "382", "480", "728", "902", "1334", "1698", "2404", "3148", "4292", "5742", "7608", "10304", "13430", "18192", "23592", "31720", "41144", "54766", "71188", "93762", "122156", "159420", "207820", "269380", "350726", "452434", "587520", "755446" ]
[ "nonn" ]
11
0
4
[ "A080054", "A156616", "A263149", "A263150", "A270919", "A291697", "A361008" ]
null
Vaclav Kotesovec, Apr 20 2023
2023-04-21T02:49:49
oeisdata/seq/A361/A361008.seq
cd1a70ca98b3eb1987fcc09a9f741693
A361009
Positive integers k such that 2*k cannot be expressed p^2-q where p and q are primes.
[ "5", "8", "14", "17", "20", "26", "29", "32", "35", "38", "41", "44", "47", "50", "53", "56", "62", "65", "68", "71", "72", "74", "77", "80", "86", "89", "92", "95", "98", "101", "104", "107", "110", "113", "116", "119", "122", "125", "128", "131", "134", "137", "140", "146", "149", "152", "155", "158", "161", "164", "167", "170", "173", "176", "182", "185", "188", "191", "194", "197" ]
[ "nonn" ]
5
1
1
[ "A000040", "A001248", "A008585", "A016789", "A109619", "A361009" ]
null
Michel Marcus, Feb 28 2023
2023-02-28T08:21:01
oeisdata/seq/A361/A361009.seq
e5a8468da0ce6a13c790b3644cc24494
A361010
Decimal expansion of conventional value of ohm-90 (Omega_{90}).
[ "1", "0", "0", "0", "0", "0", "0", "0", "1", "7", "7", "9", "3", "6", "6", "7", "5", "6", "4", "3", "2", "3", "6", "1", "3", "3", "4", "0", "6", "9", "8", "9", "5", "7", "8", "0", "9", "6", "8", "1", "7", "3", "1", "7", "5", "5", "1", "4", "7", "8", "7", "7", "6", "3", "1", "7", "6", "3", "5", "5", "5", "0", "4", "7", "4", "3", "1", "6", "4", "7", "6", "2", "2", "3", "8", "2", "6", "6", "9", "0", "5", "7", "7", "3", "8", "7", "4" ]
[ "cons", "nonn", "easy" ]
13
1
10
[ "A248510", "A361010" ]
null
Marco Ripà, Feb 28 2023
2025-02-13T04:06:21
oeisdata/seq/A361/A361010.seq
4a7fbeeb6e2a50cfa17563a9daa4e844
A361011
Decimal expansion of conventional value of ampere-90 (A_{90}).
[ "1", "0", "0", "0", "0", "0", "0", "0", "8", "8", "8", "7", "1", "4", "3", "8", "1", "0", "4", "9", "1", "8", "0", "1" ]
[ "cons", "nonn", "fini", "full" ]
8
1
9
[ "A248508", "A248510", "A361011" ]
null
Marco Ripà, Feb 28 2023
2025-02-13T04:02:49
oeisdata/seq/A361/A361011.seq
65e7725e7ca93640243f41400c2e13c0
A361012
Multiplicative with a(p^e) = sigma(e), where sigma = A000203.
[ "1", "1", "1", "3", "1", "1", "1", "4", "3", "1", "1", "3", "1", "1", "1", "7", "1", "3", "1", "3", "1", "1", "1", "4", "3", "1", "4", "3", "1", "1", "1", "6", "1", "1", "1", "9", "1", "1", "1", "4", "1", "1", "1", "3", "3", "1", "1", "7", "3", "3", "1", "3", "1", "4", "1", "4", "1", "1", "1", "3", "1", "1", "3", "12", "1", "1", "1", "3", "1", "1", "1", "12", "1", "1", "3", "3", "1", "1", "1", "7", "7", "1", "1", "3", "1", "1" ]
[ "nonn", "mult" ]
27
1
4
[ "A000203", "A049419", "A072911", "A145353", "A327837", "A327838", "A361012" ]
null
Vaclav Kotesovec, Feb 28 2023
2025-01-08T02:08:39
oeisdata/seq/A361/A361012.seq
137062a0cf2310c30c6b715eedb425f1
A361013
Decimal expansion of a constant related to the asymptotics of A361012.
[ "2", "9", "6", "0", "0", "8", "0", "3", "0", "2", "0", "2", "4", "9", "4", "1", "4", "1", "0", "4", "8", "1", "8", "2", "0", "4", "7", "8", "1", "1", "0", "8", "9", "4", "6", "9", "3", "9", "2", "8", "4", "3", "9", "0", "9", "5", "9", "2", "5", "1", "6", "3", "4", "1", "1", "9", "6", "7", "5", "0", "4", "4", "8", "0", "8", "6", "6", "3", "3", "9", "3", "5", "7", "8", "7", "3", "7", "3", "8", "2", "4", "9", "5", "8", "4", "6", "2", "6", "7", "3", "8", "5", "0", "1", "0", "8", "0", "5", "1", "7", "8", "6", "0", "6", "6" ]
[ "nonn", "cons" ]
10
1
1
[ "A327837", "A327838", "A361012", "A361013" ]
null
Vaclav Kotesovec, Feb 28 2023
2023-02-28T07:46:22
oeisdata/seq/A361/A361013.seq
a4b9f08869124c8318c4b7f59702e047
A361014
Triangle read by rows: T(n,k) is the k-th Lie-Betti number of the hypercube graph on 2^(n-1) vertices, n >= 1, k >= 0.
[ "1", "1", "1", "2", "2", "1", "1", "4", "14", "25", "28", "25", "14", "4", "1", "1", "8", "64", "258", "986", "2870", "6134", "11586", "18830", "23832", "25078", "23832", "18830", "11586", "6134", "2870", "986", "258", "64", "8", "1" ]
[ "nonn", "tabf", "more" ]
15
1
4
[ "A088459", "A360571", "A360572", "A360625", "A360936", "A360937", "A361014" ]
null
Samuel J. Bevins, Feb 28 2023
2023-02-28T18:16:24
oeisdata/seq/A361/A361014.seq
4c00fae92fa34c4322a632198cacc423
A361015
Number of arithmetic progressions of 3 or more integers whose product is equal to n.
[ "0", "2", "0", "0", "2", "0", "3", "2", "2", "0", "0", "0", "0", "4", "2", "0", "0", "0", "0", "2", "0", "0", "10", "0", "0", "1", "2", "0", "0", "0", "1", "0", "0", "2", "2", "0", "0", "0", "4", "0", "2", "0", "0", "4", "0", "0", "6", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "2", "0", "0", "2", "5", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "2", "0", "6", "4", "0", "0", "0", "0", "0", "0", "0", "0", "2", "2", "0", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "14", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "20" ]
[ "nonn" ]
22
2
2
[ "A062011", "A146208", "A361015" ]
null
Antti Karttunen, Feb 28 2023
2023-05-11T23:39:21
oeisdata/seq/A361/A361015.seq
6c1cbc204ed7c02bfe5cafb0f32c0540
A361016
a(n) = 1 if A004718(n) = 0, otherwise 0, where A004718 is the Danish composer Per Nørgård's "infinity sequence".
[ "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0" ]
[ "nonn" ]
14
0
null
[ "A004718", "A083866", "A343029", "A343030", "A361016" ]
null
Antti Karttunen, Mar 02 2023
2023-03-03T17:53:33
oeisdata/seq/A361/A361016.seq
712671435179e18e873edd0366eaa77f
A361017
Dirichlet inverse of Thue-Morse sequence, A010060.
[ "1", "-1", "0", "0", "0", "0", "-1", "0", "0", "0", "-1", "0", "-1", "1", "0", "0", "0", "0", "-1", "0", "-1", "1", "0", "0", "-1", "1", "0", "0", "0", "0", "-1", "0", "0", "0", "-1", "0", "-1", "1", "0", "0", "-1", "1", "0", "0", "0", "0", "-1", "0", "0", "1", "0", "0", "0", "0", "-1", "0", "0", "0", "-1", "0", "-1", "1", "0", "0", "0", "0", "-1", "0", "-1", "1", "0", "0", "-1", "1", "0", "0", "2", "0", "-1", "0", "-1", "1", "0", "0", "0", "0", "-1", "0", "0", "0", "1", "0", "-1", "1", "0", "0", "-1", "0", "0", "0", "0", "0", "-1", "0", "0" ]
[ "sign" ]
9
1
77
[ "A010060", "A361017", "A361018" ]
null
Antti Karttunen, Mar 02 2023
2023-03-03T17:53:40
oeisdata/seq/A361/A361017.seq
5758b39a473ec978470d63c22dac62c8
A361018
Parity of A361017, where A361017 is the Dirichlet inverse of Thue-Morse sequence, A010060.
[ "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "0", "1", "0", "1", "1", "0", "0" ]
[ "nonn" ]
11
1
null
[ "A000035", "A010060", "A323886", "A361017", "A361018" ]
null
Antti Karttunen, Mar 02 2023
2023-03-03T17:53:44
oeisdata/seq/A361/A361018.seq
950ae570c2baa0ed112138127f35c400
A361019
Dirichlet inverse of A038712.
[ "1", "-3", "-1", "2", "-1", "3", "-1", "0", "0", "3", "-1", "-2", "-1", "3", "1", "0", "-1", "0", "-1", "-2", "1", "3", "-1", "0", "0", "3", "0", "-2", "-1", "-3", "-1", "0", "1", "3", "1", "0", "-1", "3", "1", "0", "-1", "-3", "-1", "-2", "0", "3", "-1", "0", "0", "0", "1", "-2", "-1", "0", "1", "0", "1", "3", "-1", "2", "-1", "3", "0", "0", "1", "-3", "-1", "-2", "1", "-3", "-1", "0", "-1", "3", "0", "-2", "1", "-3", "-1", "0", "0", "3", "-1", "2", "1", "3", "1", "0", "-1", "0", "1", "-2", "1", "3", "1", "0", "-1" ]
[ "sign", "mult" ]
9
1
2
[ "A038712", "A361019" ]
null
Antti Karttunen, Mar 02 2023
2023-03-03T17:53:48
oeisdata/seq/A361/A361019.seq
bd9c9e61a5d2421cf485ca01eeff2e48
A361020
Lexicographically earliest infinite sequence such that a(i) = a(j) => A343029(i) = A343029(j) and A343030(i) = A343030(j) for all i, j >= 0.
[ "1", "2", "3", "4", "2", "5", "6", "7", "3", "4", "5", "8", "4", "9", "10", "11", "2", "5", "6", "7", "5", "8", "9", "12", "6", "7", "8", "13", "7", "14", "15", "16", "3", "4", "5", "8", "4", "9", "10", "11", "5", "8", "9", "12", "8", "13", "14", "17", "4", "9", "10", "11", "9", "12", "13", "18", "10", "11", "12", "19", "11", "20", "21", "22", "2", "5", "6", "7", "5", "8", "9", "12", "6", "7", "8", "13", "7", "14", "15", "16", "5", "8", "9", "12", "8", "13", "14", "17", "9", "12", "13", "18", "12", "19", "20", "23", "6", "7", "8" ]
[ "nonn", "look" ]
13
0
2
[ "A000120", "A004718", "A286622", "A343029", "A343030", "A361016", "A361020" ]
null
Antti Karttunen, Mar 03 2023
2023-03-04T17:07:41
oeisdata/seq/A361/A361020.seq
465f1012a0563f47ffc3739848a64939
A361021
Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(i) = A007814(j), A001065(i) = A001065(j) and A051953(i) = A051953(j), for all i, j >= 1.
[ "1", "2", "3", "4", "3", "5", "3", "6", "7", "8", "3", "9", "3", "10", "11", "12", "3", "13", "3", "14", "15", "16", "3", "17", "18", "19", "20", "21", "3", "22", "3", "23", "24", "25", "26", "27", "3", "28", "29", "30", "3", "31", "3", "32", "33", "34", "3", "35", "36", "37", "38", "39", "3", "40", "29", "41", "42", "43", "3", "44", "3", "45", "46", "47", "48", "49", "3", "50", "51", "52", "3", "53", "3", "54", "55", "56", "48", "57", "3", "58", "59", "60", "3", "61", "42", "62", "63", "64", "3", "65", "38", "66", "67", "68", "69", "70", "3", "71" ]
[ "nonn" ]
9
1
2
[ "A001065", "A007814", "A051953", "A305801", "A305895", "A319346", "A353520", "A353560", "A361021" ]
null
Antti Karttunen, Mar 03 2023
2023-03-04T17:07:45
oeisdata/seq/A361/A361021.seq
175fc493778b0f64731410cd6e0b000b
A361022
a(n) = 1 if d(n) divides d(n+1), otherwise 0, where d(n) is number of positive divisors of n.
[ "1", "1", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "1", "0", "0", "1", "0", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "1", "1", "0", "1", "0", "0", "0", "1", "1", "1", "0", "1", "1", "0", "0", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "1", "0", "1", "1", "0", "0", "1" ]
[ "nonn" ]
9
1
null
[ "A000005", "A057922", "A361022" ]
null
Antti Karttunen, Mar 02 2023
2023-03-04T17:07:49
oeisdata/seq/A361/A361022.seq
90f67a9f1dc76ec206d4371eaaec56db
A361023
a(n) = 1 if A007814(sigma(n)) >= A007814(n), otherwise 0, where A007814(n) gives the 2-adic valuation of n.
[ "1", "0", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "0", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "0", "1", "0", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "0", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1" ]
[ "nonn" ]
20
1
null
[ "A000035", "A000203", "A007814", "A017666", "A216781", "A319338", "A319346", "A324903", "A336937", "A361023", "A361024", "A361025" ]
null
Antti Karttunen, Mar 03 2023
2023-03-04T17:07:53
oeisdata/seq/A361/A361023.seq
dbf617bff6565f37b67d568ea5153f6f
A361024
a(n) = 1 if n and sigma(n) have equal 2-adic valuations, otherwise 0, where sigma is the sum of divisors function.
[ "1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1" ]
[ "nonn" ]
14
1
null
[ "A000203", "A003961", "A007814", "A010052", "A216780", "A319346", "A324903", "A336937", "A361024", "A361025" ]
null
Antti Karttunen, Mar 03 2023
2023-03-04T17:07:57
oeisdata/seq/A361/A361024.seq
0d4489640072c9ee07aa1c9e3adeea3e
A361025
a(n) = A007814(sigma(n)) - A007814(n), where A007814(n) gives the 2-adic valuation of n, and sigma is the sum of divisors function.
[ "0", "-1", "2", "-2", "1", "1", "3", "-3", "0", "0", "2", "0", "1", "2", "3", "-4", "1", "-1", "2", "-1", "5", "1", "3", "-1", "0", "0", "3", "1", "1", "2", "5", "-5", "4", "0", "4", "-2", "1", "1", "3", "-2", "1", "4", "2", "0", "1", "2", "4", "-2", "0", "-1", "3", "-1", "1", "2", "3", "0", "4", "0", "2", "1", "1", "4", "3", "-6", "2", "3", "2", "-1", "5", "3", "3", "-3", "1", "0", "2", "0", "5", "2", "4", "-3", "0", "0", "2", "3", "2", "1", "3", "-1", "1", "0", "4", "1", "7", "3", "3", "-3", "1", "-1", "2", "-2", "1", "2", "3", "-2", "6" ]
[ "sign" ]
18
1
3
[ "A000203", "A007814", "A216780", "A216781", "A216782", "A324903", "A336937", "A361024", "A361025" ]
null
Antti Karttunen, Mar 03 2023
2023-11-23T15:12:13
oeisdata/seq/A361/A361025.seq
b3029d9e83fa8a8cf039e0adda66debd
A361026
Lexicographically earliest infinite sequence such that a(i) = a(j) => A003557(i) = A003557(j) and A053669(i) = A053669(j), for all i, j >= 1.
[ "1", "2", "1", "3", "1", "4", "1", "5", "6", "2", "1", "7", "1", "2", "1", "8", "1", "9", "1", "3", "1", "2", "1", "10", "11", "2", "12", "3", "1", "13", "1", "14", "1", "2", "1", "15", "1", "2", "1", "5", "1", "4", "1", "3", "6", "2", "1", "16", "17", "18", "1", "3", "1", "19", "1", "5", "1", "2", "1", "20", "1", "2", "6", "21", "1", "4", "1", "3", "1", "2", "1", "22", "1", "2", "11", "3", "1", "4", "1", "8", "23", "2", "1", "7", "1", "2", "1", "5", "1", "24", "1", "3", "1", "2", "1", "25", "1", "26", "6", "27", "1", "4", "1", "5", "1" ]
[ "nonn" ]
7
1
2
[ "A003557", "A007814", "A053669", "A305801", "A353520", "A361026" ]
null
Antti Karttunen, Mar 03 2023
2023-03-04T17:08:36
oeisdata/seq/A361/A361026.seq
32cd413141951bbd38bac2b95aae6026
A361027
Table of generalized de Bruijn's numbers (A006480) read by ascending antidiagonals.
[ "2", "30", "3", "560", "20", "20", "11550", "210", "75", "210", "252252", "2772", "504", "504", "2772", "5717712", "42042", "4620", "2352", "4620", "42042", "133024320", "700128", "51480", "15840", "15840", "51480", "700128", "3155170590", "12471030", "656370", "135135", "81675", "135135", "656370", "12471030", "75957810500", "233716340", "9237800" ]
[ "nonn", "tabl", "easy" ]
17
0
1
[ "A006480", "A024488", "A135573", "A208881", "A361027", "A361028", "A361029", "A361030", "A361031" ]
null
Peter Bala, Feb 28 2023
2023-03-13T07:20:50
oeisdata/seq/A361/A361027.seq
49aadaa84736d0fd5072c98779309ed4
A361028
a(n) = 2*(3*n)!/(n!*(n+1)!^2).
[ "2", "3", "20", "210", "2772", "42042", "700128", "12471030", "233716340", "4557468630", "91752013080", "1896208270320", "40055997189600", "862021408906800", "18849534808095360", "417929529573239310", "9379553386892837940", "212776905535994934750", "4873239487455972633000", "112571832160232967822300" ]
[ "nonn", "tabl", "easy" ]
18
0
1
[ "A000108", "A006480", "A007226", "A361027", "A361028", "A361029", "A361030", "A361031", "A361033" ]
null
Peter Bala, Feb 28 2023
2023-03-13T07:21:11
oeisdata/seq/A361/A361028.seq
008c8a9c8c2ea4fb87989921a6b74d49
A361029
a(n) = 120*(3*n)!/(n!*(n+2)!^2).
[ "30", "20", "75", "504", "4620", "51480", "656370", "9237800", "140229804", "2259901800", "38230005450", "673210036800", "12262039956000", "229872375708480", "4417859720647350", "86767376381987400", "1736954330906081100", "35364582637561485000", "730985923118395894950", "15315895532004485418000" ]
[ "nonn", "easy" ]
14
0
1
[ "A006480", "A007054", "A361027", "A361028", "A361029", "A361030", "A361031", "A361037" ]
null
Peter Bala, Mar 01 2023
2023-07-02T19:10:45
oeisdata/seq/A361/A361029.seq
1d48403142f1a49a728de118250085ed
A361030
a(n) = 20160*(3*n)!/(n!*(n+3)!^2).
[ "560", "210", "504", "2352", "15840", "135135", "1361360", "15519504", "194699232", "2636552100", "38003792400", "577037174400", "9155656500480", "150853746558690", "2568167588473200", "44990491457326800", "808333317429976800", "14853124707775823700", "278470827854627007600", "5316261259042879236000" ]
[ "nonn", "easy" ]
19
0
1
[ "A006480", "A007272", "A361027", "A361028", "A361029", "A361030", "A361031", "A361038" ]
null
Peter Bala, Mar 01 2023
2024-10-05T19:59:58
oeisdata/seq/A361/A361030.seq
ecf6b216f53efb148b6b8cdfa0cb82e6
A361031
a(n) = (3^3)*(1*2*4*5*7*8*10*11)*(3*n)!/(n!*(n+4)!^2).
[ "11550", "2772", "4620", "15840", "81675", "550550", "4492488", "42325920", "446185740", "5148297000", "63985977000", "846321189120", "11802213457650", "172255143129300", "2615726247519000", "41127042052404000", "666874986879730860", "11114583114662181000", "189866473537245687000", "3316382259894423720000" ]
[ "nonn", "easy" ]
17
0
1
[ "A006480", "A348893", "A361027", "A361028", "A361029", "A361030", "A361031" ]
null
Peter Bala, Mar 01 2023
2023-04-24T13:40:06
oeisdata/seq/A361/A361031.seq
16bdebefa7cb6022f772f252e9d17028
A361032
Square array read by ascending antidiagonals: T(n,k) = F(n) * (4*k)!/(k!*(k + n + 1)!^3), where F(n) = (1/8)*(4*n + 4)!/(n + 1)!; n, k >= 0.
[ "3", "315", "9", "46200", "280", "280", "7882875", "17325", "3675", "17325", "1466593128", "1513512", "116424", "116424", "1513512", "288592936632", "162954792", "5885880", "2134440", "5885880", "162954792", "59064793444800", "20193091776", "399072960", "67953600", "67953600", "399072960", "20193091776", "12445136556298875" ]
[ "nonn", "tabl", "easy" ]
16
0
1
[ "A008977", "A135573", "A361027", "A361032", "A361033", "A361034", "A361035" ]
null
Peter Bala, Mar 04 2023
2024-01-05T14:27:22
oeisdata/seq/A361/A361032.seq
888b88df679f16e9a664948e43ec008d
A361033
a(n) = 3*(4*n)!/(n!*(n+1)!^3).
[ "3", "9", "280", "17325", "1513512", "162954792", "20193091776", "2768662192725", "409716429837000", "64358256798795960", "10605621798062141760", "1817833036248401270280", "321997225483126007438400", "58649494641569379926280000", "10941649720331183519046796800", "2084191938036600263793119045925" ]
[ "nonn", "easy" ]
14
0
1
[ "A000108", "A007226", "A007228", "A008977", "A361028", "A361032", "A361033", "A361034", "A361035" ]
null
Peter Bala, Mar 01 2023
2024-07-30T11:23:10
oeisdata/seq/A361/A361033.seq
948cbbfe6a33ff4a645b728cc9e69ab3
A361034
a(n) = 2520*(4*n)!/(n!*(n+2)!^3).
[ "315", "280", "3675", "116424", "5885880", "399072960", "33129291195", "3190228041000", "344161801063080", "40616781150254400", "5155510596280207800", "695029472211496161600", "98570579229528369624000", "14597207555235045670540800", "2243893009052293495117018875", "356344642367340570239409729000" ]
[ "nonn", "easy" ]
13
0
1
[ "A007054", "A008977", "A361029", "A361032", "A361033", "A361034", "A361035" ]
null
Peter Bala, Mar 01 2023
2023-03-15T12:40:57
oeisdata/seq/A361/A361034.seq
037f4dbd903dd1a69da168cac99dc0df
A361035
a(n) = 9979200 * (4*n)!/(n!*(n+3)!^3).
[ "46200", "17325", "116424", "2134440", "67953600", "3086579925", "179961581800", "12633303042360", "1023952465972800", "93080123469333000", "9292590788015304000", "1003030870975774344000", "115656146295979953692160", "14112534648127632044761125", "1808633485822731984665865000" ]
[ "nonn", "easy" ]
9
0
1
[ "A007272", "A008977", "A361030", "A361032", "A361033", "A361034", "A361035" ]
null
Peter Bala, Mar 01 2023
2023-03-15T12:40:52
oeisdata/seq/A361/A361035.seq
cda931812e7a82ef949dedf2aea54b2c
A361036
a(n) = n! * [x^n] (1 + x)^n * exp(x*(1 + x)^n).
[ "1", "2", "11", "124", "2225", "56546", "1928707", "85029596", "4687436609", "314255427490", "25077179715131", "2343489559096412", "253185531592066801", "31279831940279656514", "4376923336721600128115", "687815536092999747916156", "120491486068612766739548417", "23378730923206887237941740226" ]
[ "nonn", "easy" ]
13
0
2
[ "A047974", "A278070", "A361036", "A361281" ]
null
Peter Bala, Mar 13 2023
2023-03-28T07:37:49
oeisdata/seq/A361/A361036.seq
27ba96f57bde88567a48e197d2ca50b3
A361037
a(n) = 20*(3*n)!/((2*n)!*(n+2)!).
[ "10", "10", "25", "84", "330", "1430", "6630", "32300", "163438", "852150", "4552275", "24812400", "137547000", "773564328", "4405019090", "25357898940", "147375745990", "863805209750", "5101386767295", "30332569967700", "181465130121450", "1091677288630950" ]
[ "nonn", "easy" ]
18
0
1
[ "A000139", "A001764", "A005809", "A007226", "A361037", "A361038", "A361039" ]
null
Peter Bala, Mar 04 2023
2024-08-05T15:35:09
oeisdata/seq/A361/A361037.seq
1aac50aa1550032831bd0da0bebd091b
A361038
a(n) = 1680 * (3*n)!/((2*n)!*(n+3)!).
[ "280", "210", "420", "1176", "3960", "15015", "61880", "271320", "1248072", "5965050", "29414700", "148874400", "770263200", "4061212722", "21765976680", "118336861720", "651555929640", "3627981880950", "20405547069180", "115815267149400", "662742214356600" ]
[ "nonn", "easy" ]
14
0
1
[ "A000139", "A001764", "A007226", "A007272", "A361037", "A361038", "A361039", "A361040" ]
null
Peter Bala, Mar 04 2023
2023-03-07T11:54:40
oeisdata/seq/A361/A361038.seq
036479c380e963bc89c701601e231a16
A361039
a(n) = 55440 * (3*n)!/((2*n)!*(n+4)!).
[ "2310", "1386", "2310", "5544", "16335", "55055", "204204", "813960", "3432198", "15142050", "69334650", "327523680", "1588667850", "7883530578", "39904290580", "205532444040", "1075067283906", "5701114384350", "30608320603770", "166169731127400", "911270544740325" ]
[ "nonn", "easy" ]
14
0
1
[ "A000139", "A001764", "A007226", "A007272", "A361037", "A361038", "A361039", "A361041" ]
null
Peter Bala, Mar 04 2023
2023-03-07T11:54:37
oeisdata/seq/A361/A361039.seq
73ddf20cc4b81a8ecaff4cf4f3598747
A361040
a(n) = 420*(3*n)!/(n!*(2*n + 3)!).
[ "70", "21", "30", "70", "210", "735", "2856", "11970", "53130", "246675", "1187550", "5890248", "29954680", "155602020", "823184880", "4424618730", "24116031162", "133072694475", "742405558650", "4182821562150", "23776769743650", "136248095712855", "786482994679200" ]
[ "nonn", "easy" ]
12
0
1
[ "A000139", "A001764", "A005809", "A007272", "A135573", "A361038", "A361040", "A361041" ]
null
Peter Bala, Mar 04 2023
2024-07-28T03:44:13
oeisdata/seq/A361/A361040.seq
7a4c60e6621c29f0538bf29e697d83b2
A361041
a(n) = 1680*(3*n)!/(n!*(2*n + 4)!).
[ "70", "14", "15", "28", "70", "210", "714", "2660", "10626", "44850", "197925", "906192", "4279240", "20746936", "102898110", "520543380", "2679559018", "14007652050", "74240555865", "398363958300", "2161524522150", "11847660496770", "65540249556600", "365634339159024" ]
[ "nonn", "easy" ]
8
0
1
[ "A000139", "A001764", "A005809", "A348893", "A361039", "A361040", "A361041" ]
null
Peter Bala, Mar 04 2023
2023-03-07T11:54:28
oeisdata/seq/A361/A361041.seq
bdb6b62e129c6f30baf54c6bc27ce0eb
A361042
Triangle read by rows: T(n, k) = Sum_{j=0..n} j! * binomial(n - j, n - k).
[ "1", "1", "2", "1", "3", "4", "1", "4", "7", "10", "1", "5", "11", "17", "34", "1", "6", "16", "28", "51", "154", "1", "7", "22", "44", "79", "205", "874", "1", "8", "29", "66", "123", "284", "1079", "5914", "1", "9", "37", "95", "189", "407", "1363", "6993", "46234", "1", "10", "46", "132", "284", "596", "1770", "8356", "53227", "409114", "1", "11", "56", "178", "416", "880", "2366", "10126", "61583", "462341", "4037914" ]
[ "nonn", "tabl" ]
10
0
3
[ "A003422", "A014144", "A133942", "A152689", "A233449", "A293468", "A361042" ]
null
Peter Luschny, Mar 13 2023
2024-03-28T21:56:46
oeisdata/seq/A361/A361042.seq
a2a989f2196eaa8a9eb02e7363c1d840
A361043
Array read by descending antidiagonals. A(n, k) is, if n > 0, the number of multiset permutations of {0, 1} of length n * k where the number of occurrences of 1 are multiples of n. A(0, k) = k + 1.
[ "1", "2", "1", "3", "2", "1", "4", "4", "2", "1", "5", "8", "8", "2", "1", "6", "16", "32", "22", "2", "1", "7", "32", "128", "170", "72", "2", "1", "8", "64", "512", "1366", "992", "254", "2", "1", "9", "128", "2048", "10922", "16512", "6008", "926", "2", "1", "10", "256", "8192", "87382", "261632", "215766", "37130", "3434", "2", "1", "11", "512", "32768", "699050", "4196352", "6643782", "2973350", "232562", "12872", "2", "1" ]
[ "nonn", "tabl" ]
19
0
2
[ "A000027", "A000079", "A007613", "A070775", "A070782", "A070832", "A070833", "A070967", "A081294", "A094211", "A094213", "A167009", "A308500", "A361043" ]
null
Peter Luschny, Mar 18 2023
2023-03-20T14:14:49
oeisdata/seq/A361/A361043.seq
ab2838b570689677349df711cc87dea1
A361044
Triangle read by rows. T(n, k) is the k-th Lie-Betti number of the friendship (or windmill) graph, for n >= 1.
[ "1", "3", "8", "12", "8", "3", "1", "1", "5", "24", "60", "109", "161", "161", "109", "60", "24", "5", "1", "1", "7", "48", "168", "483", "1074", "1805", "2531", "2886", "2531", "1805", "1074", "483", "168", "48", "7", "1" ]
[ "nonn", "tabf", "more" ]
11
1
2
[ "A088459", "A360571", "A360572", "A360625", "A360936", "A360937", "A361044" ]
null
Peter Luschny, Mar 01 2023
2023-03-18T08:49:14
oeisdata/seq/A361/A361044.seq
0852bfa3dcec02ddbf7f0fb4697c3631
A361045
Array read by descending antidiagonals. A(n, k) is, if n > 0, the number of multiset combinations of {0, 1} whose type is defined in the comments. A(0, k) = k + 1.
[ "1", "2", "1", "3", "4", "1", "4", "10", "6", "1", "5", "20", "19", "8", "1", "6", "35", "44", "30", "10", "1", "7", "56", "85", "76", "43", "12", "1", "8", "84", "146", "155", "116", "58", "14", "1", "9", "120", "231", "276", "245", "164", "75", "16", "1", "10", "165", "344", "448", "446", "355", "220", "94", "18", "1", "11", "220", "489", "680", "735", "656", "485", "284", "115", "20", "1" ]
[ "nonn", "tabl" ]
14
0
2
[ "A000012", "A000027", "A000292", "A005843", "A005900", "A028878", "A100175", "A336288", "A361043", "A361045", "A361682" ]
null
Peter Luschny, Mar 21 2023
2023-03-23T07:57:47
oeisdata/seq/A361/A361045.seq
ba9bf42bfd8afd62b64294fa23bc982a
A361046
Expansion of g.f. A(x) satisfying A(x) = Sum_{n>=0} d^n/dx^n x^(3*n) * A(x)^(2*n) / n!.
[ "1", "3", "45", "1113", "36459", "1448568", "66726309", "3469988835", "200242815669", "12670449226269", "871389659249424", "64693985439491127", "5156607707368927875", "439261264283443326927", "39831856169938193953827", "3831650468281643037364389", "389807188331526942149375433" ]
[ "nonn" ]
28
0
2
[ "A088714", "A229619", "A303063", "A356848", "A360950", "A360973", "A360974", "A360975", "A360976", "A361046", "A361047" ]
null
Paul D. Hanna, Mar 03 2023
2023-03-15T03:03:17
oeisdata/seq/A361/A361046.seq
29bcac21b59b6bf5f54e41769f3ea36c
A361047
Expansion of g.f. A(x) satisfying A(x) = Series_Reversion(x - x^3*A'(x)^2).
[ "1", "1", "9", "159", "4051", "131688", "5132793", "231332589", "11778989157", "666865748751", "41494745678544", "2812781975630049", "206264308294757115", "16268935714201604701", "1373512281722006688063", "123601628009085259269819", "11812339040349301277253801", "1194940136210629914238593762" ]
[ "nonn" ]
16
1
3
[ "A229619", "A360977", "A360978", "A361046", "A361047" ]
null
Paul D. Hanna, Mar 03 2023
2023-03-05T07:02:51
oeisdata/seq/A361/A361047.seq
7dab30373b7ac83e68e94be229c83ca6
A361048
Expansion of g.f. A(x) satisfying a(n) = [x^(n-1)] A(x)^(n+1) for n >= 1.
[ "1", "1", "3", "18", "160", "1830", "25074", "395248", "6990876", "136464705", "2906040280", "66938704602", "1656963703434", "43848218457953", "1235194571623950", "36905133359883240", "1165832901366137184", "38830278855693956931", "1360186936717777641747", "49995325008141402758320" ]
[ "nonn" ]
13
0
3
[ "A113882", "A132070", "A361048", "A361049" ]
null
Paul D. Hanna, Mar 13 2023
2023-05-04T20:37:39
oeisdata/seq/A361/A361048.seq
ae9c038de8190c58835389c463b04437
A361049
G.f. satisfies: A(x) = (1/x)*Series_Reversion( x/(1 + x*A(x)^2 + x^2*A(x)*A'(x)) ).
[ "1", "1", "4", "28", "269", "3201", "44737", "711691", "12630023", "246594988", "5244025502", "120540052304", "2976918491501", "78601791684495", "2209667973082374", "65901745111752843", "2078619947109354811", "69141776287740239348", "2419303138068147399700", "88842295496847889690405" ]
[ "nonn" ]
7
0
3
[ "A113882", "A132070", "A361048", "A361049" ]
null
Paul D. Hanna, Mar 13 2023
2023-03-13T12:47:24
oeisdata/seq/A361/A361049.seq
08dbca4915319957e688ca16ad654c43
A361050
Expansion of g.f. A(x,y) satisfying y/x = Sum_{n=-oo..+oo} x^(n*(3*n+1)/2) * (A(x,y)^(3*n) - 1/A(x,y)^(3*n+1)), as a triangle read by rows.
[ "1", "0", "1", "0", "5", "4", "0", "18", "40", "22", "0", "55", "244", "335", "140", "0", "149", "1160", "2924", "2875", "969", "0", "371", "4688", "19090", "32745", "25081", "7084", "0", "867", "16848", "103110", "272250", "352814", "221397", "53820", "0", "1923", "55332", "485356", "1839075", "3565548", "3709244", "1971775", "420732", "0", "4086", "169048", "2054520", "10674985", "28909300", "44146487", "38344384", "17682895", "3362260" ]
[ "nonn", "tabl" ]
21
1
5
[ "A002293", "A356500", "A359921", "A359924", "A360191", "A361050", "A361051", "A361052", "A361535", "A361538", "A361550" ]
null
Paul D. Hanna, Mar 18 2023
2024-01-05T23:33:12
oeisdata/seq/A361/A361050.seq
b07d6c4cda7c1157c04d699fac6413af
A361051
Expansion of g.f. A(x) satisfying 3/x = Sum_{n=-oo..+oo} x^(n*(3*n+1)/2) * (A(x)^(3*n) - 1/A(x)^(3*n+1)).
[ "1", "3", "51", "1008", "22746", "558177", "14469999", "389827008", "10805735061", "306185433921", "8828873667975", "258229614694974", "7642514652514140", "228450735379271754", "6887262023421308658", "209169231039167908596", "6393531094406983438776", "196536271435928605186752", "6071932630099467279020415" ]
[ "nonn" ]
13
1
2
[ "A359921", "A359924", "A361050", "A361051", "A361052", "A361538" ]
null
Paul D. Hanna, Mar 18 2023
2024-01-05T17:17:49
oeisdata/seq/A361/A361051.seq
5d2d4c93a333a5e7e3eafd1b02a40f35
A361052
Expansion of g.f. A(x) satisfying 4/x = Sum_{n=-oo..+oo} x^(n*(3*n+1)/2) * (A(x)^(3*n) - 1/A(x)^(3*n+1)).
[ "1", "4", "84", "2120", "61404", "1934548", "64379980", "2226478604", "79225597516", "2881791020120", "106672402111192", "4005192227754984", "152168779157569376", "5839221480075313396", "225986788425426186532", "8810672964167893735292", "345722424894740010814784", "13642862904817471637398044" ]
[ "nonn" ]
11
1
2
[ "A359921", "A359924", "A361050", "A361051", "A361052" ]
null
Paul D. Hanna, Mar 18 2023
2024-01-05T16:38:03
oeisdata/seq/A361/A361052.seq
1d68df03bb75c65d1db6ea0c5d0bd201
A361053
Expansion of e.g.f. A(x) satisfying A(x) = Sum_{n>=0} (A(x)^n + 2)^n * x^n/n!.
[ "1", "3", "15", "180", "3933", "122778", "5024727", "255694050", "15594132825", "1110807585090", "90665847445059", "8355178654847874", "859198582766876661", "97668423691415577666", "12177783763614287432847", "1654751006054203510476882", "243720706148230009547388465", "38730619011753683906970442626" ]
[ "nonn" ]
9
0
2
[ "A202999", "A203013", "A361053", "A361054", "A361055", "A361056", "A361057", "A361540" ]
null
Paul D. Hanna, Feb 28 2023
2023-03-20T14:58:42
oeisdata/seq/A361/A361053.seq
e5f937749786cfa0e638d691485d6e29
A361054
Expansion of e.g.f. A(x) satisfying A(x) = Sum_{n>=0} (A(x)^n + 3)^n * x^n/n!.
[ "1", "4", "24", "328", "8480", "316064", "15448000", "940586560", "68773511680", "5883198833152", "577566163260416", "64112172571384832", "7953180924959641600", "1092205827724943429632", "164769061745517773774848", "27131359440809990936141824", "4850231804845681441360707584", "937096082325039305880612503552" ]
[ "nonn" ]
10
0
2
[ "A202999", "A203013", "A361053", "A361054", "A361055", "A361056", "A361057", "A361540" ]
null
Paul D. Hanna, Feb 28 2023
2023-03-20T15:00:00
oeisdata/seq/A361/A361054.seq
75f28b2b25269e82f36abf53e3f60215
A361055
Expansion of e.g.f. A(x) satisfying A(x) = Sum_{n>=0} (A(x)^n + 4)^n * x^n/n!.
[ "1", "5", "35", "530", "15645", "673100", "37951975", "2668045700", "225591547225", "22347122264900", "2543582111665875", "327736278022956500", "47245927138947731125", "7548695252947520166500", "1326483608786914301185375", "254733442821907695977652500", "53175506363950820566794680625", "12012490474019349963485905242500" ]
[ "nonn" ]
9
0
2
[ "A202999", "A203013", "A361053", "A361054", "A361055", "A361056", "A361057", "A361540" ]
null
Paul D. Hanna, Feb 28 2023
2023-03-20T15:00:46
oeisdata/seq/A361/A361055.seq
3bfccb4a6551252f493b644df1ae6753
A361056
Expansion of e.g.f. A(x) satisfying A(x) = Sum_{n>=0} (2*A(x)^n + 1)^n * x^n/n!.
[ "1", "3", "21", "369", "11025", "465273", "25605585", "1742552325", "141496457985", "13368820514769", "1442273097241809", "175090338669687741", "23642282811004895745", "3517444221383606541849", "572114802197326599160497", "101067684833728895205914757", "19284211878473628720362002689" ]
[ "nonn" ]
11
0
2
[ "A202999", "A203013", "A361053", "A361054", "A361055", "A361056", "A361057", "A361540" ]
null
Paul D. Hanna, Feb 28 2023
2023-03-20T15:05:47
oeisdata/seq/A361/A361056.seq
0ef00b78f0230ef12b0957af55e6b4c8
A361057
Expansion of e.g.f. A(x) satisfying A(x) = Sum_{n>=0} (3*A(x)^n + 1)^n * x^n/n!.
[ "1", "4", "40", "1000", "42208", "2511904", "194701888", "18644964160", "2128895802880", "282664859507200", "42830926407126016", "7299282818219035648", "1382930912338770866176", "288548709643121903915008", "65787364162207649519116288", "16282501210870115738111156224", "4350458941547832791800523653120" ]
[ "nonn" ]
11
0
2
[ "A202999", "A203013", "A361053", "A361054", "A361055", "A361056", "A361057", "A361540" ]
null
Paul D. Hanna, Feb 28 2023
2023-03-20T15:06:05
oeisdata/seq/A361/A361057.seq
23a2b3f42f0cc6420d756e22cf31b9c9
A361058
Least totient number k > 1 such that n*k is a nontotient number, or 0 if no such number exists.
[ "0", "0", "30", "0", "10", "0", "2", "0", "10", "110", "22", "0", "2", "22", "6", "0", "2", "0", "2", "0", "54", "22", "10", "0", "2", "22", "22", "212983792", "6" ]
[ "nonn", "more" ]
148
1
3
[ "A002202", "A007617", "A281187", "A301587", "A316665", "A329872", "A350085", "A350086", "A361058" ]
null
Jinyuan Wang, Mar 01 2023
2023-08-11T09:51:54
oeisdata/seq/A361/A361058.seq
0f4a350b0d4a6f479b03de3b29a358ec
A361059
Decimal expansion of the asymptotic mean of A000005(k)/A286324(k), the ratio between the number of divisors and the number of bi-unitary divisors.
[ "1", "1", "5", "8", "8", "5", "4", "5", "7", "2", "6", "5", "0", "3", "1", "2", "1", "0", "0", "1", "6", "4", "4", "8", "0", "1", "9", "6", "3", "9", "3", "1", "7", "5", "1", "4", "9", "0", "3", "9", "1", "0", "4", "3", "1", "8", "8", "5", "7", "3", "9", "5", "9", "6", "3", "4", "5", "2", "6", "1", "0", "6", "1", "5", "1", "4", "8", "2", "3", "3", "7", "9", "7", "4", "9", "3", "5", "4", "6", "4", "9", "0", "6", "6", "6", "5", "1", "3", "9", "2", "1", "7", "9", "2", "9", "5", "4", "7", "3", "9", "6", "2", "5", "7", "3" ]
[ "nonn", "cons" ]
7
1
3
[ "A000005", "A286324", "A307869", "A308043", "A361059", "A361060" ]
null
Amiram Eldar, Mar 01 2023
2025-02-16T08:34:04
oeisdata/seq/A361/A361059.seq
ebc7bbb1eb666643a46690d95e7c9ad9
A361060
Decimal expansion of the asymptotic mean of A286324(k)/A000005(k), the ratio between the number of bi-unitary divisors and the number of divisors.
[ "9", "0", "1", "2", "4", "1", "8", "0", "6", "8", "2", "6", "4", "8", "2", "2", "5", "5", "1", "3", "9", "1", "9", "7", "4", "8", "5", "0", "9", "4", "3", "8", "7", "5", "5", "8", "9", "8", "2", "8", "1", "1", "5", "3", "3", "8", "2", "1", "7", "8", "7", "6", "2", "8", "7", "6", "2", "6", "1", "6", "1", "2", "0", "6", "3", "0", "9", "0", "7", "3", "4", "3", "7", "3", "3", "1", "8", "6", "0", "8", "3", "7", "9", "3", "6", "3", "5", "5", "9", "5", "4", "0", "8", "6", "0", "1", "0", "5", "2", "4", "5", "6", "4", "9", "8" ]
[ "nonn", "cons" ]
6
0
1
[ "A000005", "A286324", "A307869", "A308043", "A361059", "A361060" ]
null
Amiram Eldar, Mar 01 2023
2025-02-16T08:34:04
oeisdata/seq/A361/A361060.seq
b334b13c8c311f1e791ec220a2cd8a9f
A361061
Decimal expansion of the asymptotic mean of A000005(k)/A073184(k), the ratio between the number of divisors and the number of cubefree divisors.
[ "1", "1", "0", "9", "0", "4", "9", "6", "7", "7", "9", "9", "8", "7", "3", "7", "3", "3", "6", "3", "4", "5", "2", "8", "8", "5", "8", "7", "7", "8", "1", "6", "7", "1", "7", "6", "6", "0", "0", "9", "7", "5", "2", "6", "2", "9", "6", "7", "7", "3", "0", "3", "9", "8", "3", "7", "1", "4", "2", "4", "9", "9", "7", "3", "5", "8", "1", "3", "2", "8", "8", "6", "7", "6", "1", "5", "7", "7", "5", "0", "9", "3", "4", "8", "7", "3", "2", "1", "3", "8", "2", "6", "8", "1", "7", "8", "1", "0", "0", "9", "4", "1", "3", "0", "8" ]
[ "nonn", "cons" ]
6
1
4
[ "A000005", "A073184", "A307869", "A308043", "A361061", "A361062" ]
null
Amiram Eldar, Mar 01 2023
2023-03-01T02:39:15
oeisdata/seq/A361/A361061.seq
ae93c4bfe4ac04e8e78cd307e9ea2ec7
A361062
Decimal expansion of the asymptotic mean of A073184(k)/A000005(k), the ratio between the number of cubefree divisors and the number of divisors.
[ "9", "3", "9", "9", "7", "4", "3", "5", "2", "1", "7", "6", "4", "7", "7", "0", "7", "8", "4", "7", "0", "4", "4", "2", "5", "6", "2", "3", "8", "6", "0", "2", "5", "7", "2", "6", "7", "6", "9", "8", "4", "2", "3", "1", "0", "9", "7", "7", "9", "9", "6", "7", "3", "3", "0", "5", "9", "8", "1", "3", "8", "2", "1", "6", "7", "4", "6", "1", "3", "5", "9", "5", "5", "2", "0", "4", "4", "8", "0", "1", "3", "5", "9", "2", "5", "3", "1", "3", "0", "3", "8", "4", "8", "1", "0", "5", "1", "2", "9", "4", "6", "6", "6", "7", "1" ]
[ "nonn", "cons" ]
5
0
1
[ "A000005", "A073184", "A307869", "A308043", "A361061", "A361062" ]
null
Amiram Eldar, Mar 01 2023
2023-03-01T02:39:50
oeisdata/seq/A361/A361062.seq
e53e59c79169afc283f173608ec6efa2
A361063
Multiplicative with a(p^e) = sigma_2(e), where sigma_2 = A001157.
[ "1", "1", "1", "5", "1", "1", "1", "10", "5", "1", "1", "5", "1", "1", "1", "21", "1", "5", "1", "5", "1", "1", "1", "10", "5", "1", "10", "5", "1", "1", "1", "26", "1", "1", "1", "25", "1", "1", "1", "10", "1", "1", "1", "5", "5", "1", "1", "21", "5", "5", "1", "5", "1", "10", "1", "10", "1", "1", "1", "5", "1", "1", "5", "50", "1", "1", "1", "5", "1", "1", "1", "50", "1", "1", "5", "5", "1", "1", "1", "21", "21", "1", "1", "5" ]
[ "nonn", "mult" ]
16
1
4
[ "A001157", "A049419", "A327837", "A361012", "A361013", "A361063", "A361064" ]
null
Vaclav Kotesovec, Mar 01 2023
2025-01-08T02:08:01
oeisdata/seq/A361/A361063.seq
f22f862f50db16d74e74810ea970c740
A361064
Multiplicative with a(p^e) = sigma_3(e), where sigma_3 = A001158.
[ "1", "1", "1", "9", "1", "1", "1", "28", "9", "1", "1", "9", "1", "1", "1", "73", "1", "9", "1", "9", "1", "1", "1", "28", "9", "1", "28", "9", "1", "1", "1", "126", "1", "1", "1", "81", "1", "1", "1", "28", "1", "1", "1", "9", "9", "1", "1", "73", "9", "9", "1", "9", "1", "28", "1", "28", "1", "1", "1", "9", "1", "1", "9", "252", "1", "1", "1", "9", "1", "1", "1", "252", "1", "1", "9", "9", "1", "1", "1", "73", "73", "1", "1", "9" ]
[ "nonn", "mult" ]
15
1
4
[ "A001158", "A049419", "A327837", "A361012", "A361013", "A361063", "A361064" ]
null
Vaclav Kotesovec, Mar 01 2023
2025-01-08T02:07:06
oeisdata/seq/A361/A361064.seq
edc2a0cda253148aa9940e58e7b4b5de
A361065
E.g.f. satisfies A(x) = exp( (x/(1-x)) * A(x)^2 ).
[ "1", "1", "7", "85", "1521", "36421", "1097743", "39968601", "1707558401", "83777885929", "4643185678551", "286930307457949", "19562851003118833", "1458832806486727725", "118121195050068075167", "10320576944751955718881", "967863775658734350214017", "96970880819175875321264209" ]
[ "nonn" ]
29
0
3
[ "A052868", "A361065", "A361066", "A361067", "A361068", "A361069" ]
null
Seiichi Manyama, Mar 01 2023
2025-02-16T08:34:04
oeisdata/seq/A361/A361065.seq
c771fb407f9f914d1763afce59f195dc
A361066
E.g.f. satisfies A(x) = exp( (x/(1-x)) * A(x)^3 ).
[ "1", "1", "9", "148", "3673", "123276", "5234599", "269262022", "16279709793", "1131627199816", "88926737901031", "7796168316687906", "754414052156289265", "79872584117422215484", "9184299004593618881655", "1139822558262829096519726", "151857077047173825979147969" ]
[ "nonn" ]
21
0
3
[ "A052868", "A361065", "A361066", "A361067", "A361068", "A361069" ]
null
Seiichi Manyama, Mar 01 2023
2025-02-16T08:34:04
oeisdata/seq/A361/A361066.seq
04f4230ea84ef4d71b604dfbc5be67c3
A361067
E.g.f. satisfies A(x) = exp( x/((1-x) * A(x)) ).
[ "1", "1", "1", "4", "9", "76", "175", "3606", "833", "354376", "-1605249", "65111410", "-718371071", "20105327100", "-351241054177", "9362931464446", "-214514949732735", "6039303900168976", "-165679758877120001", "5093296357218337386", "-159900268661169533119", "5405435526807425433220" ]
[ "sign" ]
22
0
4
[ "A052868", "A361065", "A361066", "A361067", "A361068", "A361069" ]
null
Seiichi Manyama, Mar 01 2023
2025-02-16T08:34:04
oeisdata/seq/A361/A361067.seq
c7b65ed47df6749b87afbbd9defbf7d1
A361068
E.g.f. satisfies A(x) = exp( x/((1-x) * A(x)^2) ).
[ "1", "1", "-1", "13", "-127", "2101", "-41801", "1030177", "-29820127", "995977801", "-37660751569", "1590847310581", "-74242656468575", "3793664894534269", "-210656932372422745", "12630986901470435401", "-813335155262348743231", "55977540398642247218449" ]
[ "sign" ]
19
0
4
[ "A052868", "A361065", "A361066", "A361067", "A361068", "A361069" ]
null
Seiichi Manyama, Mar 01 2023
2025-02-16T08:34:04
oeisdata/seq/A361/A361068.seq
987a0cb0b28cff3cadbd51c1c6ba2a00
A361069
E.g.f. satisfies A(x) = exp( x/((1-x) * A(x)^3) ).
[ "1", "1", "-3", "40", "-719", "18396", "-598157", "23713726", "-1108701519", "59735988424", "-3644505746549", "248358786667674", "-18697767289462967", "1541202721786228060", "-138046868771541971373", "13351368704222195975206", "-1386710317839048140282783", "153939247458296219191539984" ]
[ "sign" ]
21
0
3
[ "A052868", "A361065", "A361066", "A361067", "A361068", "A361069" ]
null
Seiichi Manyama, Mar 01 2023
2025-02-16T08:34:04
oeisdata/seq/A361/A361069.seq
5a9e6f1952d0d29c88f946744f0004b4
A361070
a(n) is the number of occurrences of n in A360923.
[ "1", "1", "1", "2", "4", "5", "7", "10", "12", "15", "19", "21", "27", "30", "35", "40", "44", "52", "56", "63", "70", "75", "85", "90", "100", "107", "115", "126", "132", "145", "153", "163", "175", "182", "199", "206", "220", "232", "242", "259", "268", "285", "297", "310", "328", "337", "359", "370", "387", "404", "416", "440", "451", "472", "489", "504", "528", "540" ]
[ "nonn" ]
12
0
4
[ "A002620", "A051890", "A360923", "A361070" ]
null
Rémy Sigrist, Mar 01 2023
2025-03-03T17:45:03
oeisdata/seq/A361/A361070.seq
94c402764bb8399e01e69f844954aaa5
A361071
Let c1(p) be the number of primes <= p with an odd number of 1's in base 2, and let c2(p) be the number of primes <= p with an even number of 1's in base 2. a(n) is the least prime p such that abs(c1(p) - c2(p)) >= n.
[ "2", "13", "41", "61", "67", "79", "109", "131", "137", "173", "179", "181", "191", "193", "211", "223", "227", "229", "233", "239", "241", "251", "587", "613", "617", "641", "653", "659", "661", "719", "727", "733", "761", "769", "829", "953", "967", "971", "1009", "1021", "1039", "1069", "1087", "1193", "1201", "1213", "1697", "1721", "1753", "1759", "1777", "1783", "1787" ]
[ "nonn", "base" ]
17
1
1
[ "A027697", "A027699", "A130911", "A361071" ]
null
Jean-Marc Rebert, Mar 01 2023
2023-04-07T09:26:29
oeisdata/seq/A361/A361071.seq
c3adb0cb7b5169f09baaa2070e901867
A361072
Number of assembly trees for the complete tripartite graph K_{n,n,n}.
[ "3", "672", "1065960", "5384957760", "62421991632000", "1384386516152640000", "52302971661503603040000", "3105288818333100374976000000", "273018704366102767367501606400000", "33963457896477610629976094607360000000" ]
[ "nonn" ]
13
1
1
[ "A217523", "A361072" ]
null
Eric W. Weisstein, Mar 01 2023
2025-02-16T08:34:04
oeisdata/seq/A361/A361072.seq
b14db8ad650097cc330e397cb83e15bd
A361073
Lexicographically least increasing sequence of triprimes (A014612) a(n) such that a(n) - a(n-1) and a(n) + a(n-1) are also triprimes.
[ "8", "20", "50", "125", "279", "426", "531", "539", "814", "822", "897", "1002", "1010", "1076", "1146", "1209", "1325", "1353", "1398", "1406", "1516", "1558", "1868", "1898", "1948", "1978", "1986", "2013", "2225", "2233", "2397", "2527", "2547", "2575", "2763", "2783", "2810", "2908", "2938", "2946", "3009", "3054", "3081", "3414", "3422", "3452", "3522", "3567", "3714", "3759", "3786", "3813" ]
[ "nonn" ]
38
1
1
[ "A014612", "A361073", "A361215", "A361611" ]
null
Zak Seidov and Robert Israel, Apr 09 2023
2023-04-10T01:41:00
oeisdata/seq/A361/A361073.seq
8889b723d33680497a9288c34405b822
A361074
Sum of the j-th number with binary weight n-j+1 over all j in [n].
[ "0", "1", "5", "16", "40", "92", "193", "401", "812", "1632", "3261", "6526", "13030", "26049", "52013", "103974", "207797", "415496", "830636", "1661086", "3321498", "6642591", "13283920", "26567121", "53131653", "106261922", "212518857", "425034976", "850060303", "1700115399", "3400211408", "6800412866", "13600787296" ]
[ "nonn", "base" ]
21
0
3
[ "A000120", "A057168", "A066884", "A067576", "A361074" ]
null
Alois P. Heinz, Mar 01 2023
2023-03-07T18:05:15
oeisdata/seq/A361/A361074.seq
f9ce51977cc7c6ea905db0c9152d55c3
A361075
Products of exactly 7 distinct odd primes.
[ "4849845", "5870865", "6561555", "7402395", "7912905", "8273265", "8580495", "8843835", "9444435", "10015005", "10140585", "10465455", "10555545", "10705695", "10818885", "10975965", "11565015", "11696685", "11996985", "12267255", "12777765", "12785955", "13096545", "13408395", "13498485", "13528515", "13667745", "13803405" ]
[ "nonn" ]
14
1
1
[ "A046388", "A046389", "A046390", "A046391", "A065091", "A168352", "A361075" ]
null
Karl-Heinz Hofmann, Mar 01 2023
2024-09-10T20:00:45
oeisdata/seq/A361/A361075.seq
3ea96fa78abaad9b3eee35af873cb744
A361076
Array, read by ascending antidiagonals, whose n-th row consists of the powers of 2, if n = 1; of the primes of the form (2*n-1)*2^k+1, if they exist and n > 1; and of zeros otherwise.
[ "1", "1", "2", "1", "2", "4", "2", "3", "5", "8", "1", "4", "7", "6", "16", "1", "2", "6", "13", "8", "32", "2", "3", "3", "14", "15", "12", "64", "1", "8", "5", "6", "20", "25", "18", "128", "3", "2", "10", "7", "7", "26", "39", "30", "256", "6", "15", "4", "20", "19", "11", "50", "55", "36", "512", "1", "10", "27", "9", "28", "21", "14", "52", "75", "41", "1024", "1", "4", "46", "51", "10", "82", "43", "17", "92", "85", "66", "2048" ]
[ "nonn", "tabl" ]
50
1
3
[ "A000004", "A000079", "A002253", "A002254", "A002256", "A002258", "A002261", "A032353", "A032356", "A033809", "A046067", "A279709", "A361076" ]
null
Lorenzo Sauras Altuzarra, Mar 01 2023
2023-04-01T23:57:01
oeisdata/seq/A361/A361076.seq
271ce66076468004a8e86ac15ad3f710
A361077
a(n) = largest sqrt(2*n)-smooth divisor of binomial(2*n, n).
[ "1", "1", "2", "4", "2", "36", "12", "24", "18", "4", "4", "24", "4", "200", "5400", "720", "90", "540", "300", "600", "180", "120", "120", "10800", "900", "3528", "10584", "784", "280", "1680", "112", "224", "882", "2940", "2940", "504", "28", "56", "4200", "19600", "980", "158760", "7560", "75600", "113400", "5040", "35280", "211680", "44100", "1800", "648", "432", "216", "45360", "1680" ]
[ "nonn" ]
34
0
3
[ "A263922", "A263931", "A361077" ]
null
Matthieu Pluntz, Mar 01 2023
2024-12-07T14:56:47
oeisdata/seq/A361/A361077.seq
cd24e3b6b2a06dcb4afe83b9ab82ac2e
A361078
Numbers k for which k = gcd(k', k"), where k' is the arithmetic derivative of k (A003415) and k" is the second derivative of k (A068346).
[ "4", "16", "27", "64", "108", "432", "729", "1024", "2916", "3125", "4096", "6912", "12500", "16384", "19683", "27648", "46656", "50000", "84375", "110592", "186624", "314928", "337500", "746496", "800000", "823543", "1048576", "1259712", "2125764", "2278125", "3200000", "3294172", "4194304", "5038848", "5400000", "7077888", "8503056" ]
[ "nonn" ]
20
1
1
[ "A003415", "A051674", "A068346", "A072873", "A348284", "A361078" ]
null
Marius A. Burtea, Mar 01 2023
2023-04-10T00:09:41
oeisdata/seq/A361/A361078.seq
c189ae197ffc09f413998dce50690031
A361079
Number of integers in [n .. 2n-1] having the same binary weight as n.
[ "0", "1", "1", "2", "1", "3", "3", "3", "1", "4", "4", "5", "4", "6", "6", "4", "1", "5", "5", "8", "5", "9", "9", "7", "5", "10", "10", "9", "10", "10", "10", "5", "1", "6", "6", "12", "6", "13", "13", "13", "6", "14", "14", "15", "14", "16", "16", "9", "6", "15", "15", "18", "15", "19", "19", "12", "15", "20", "20", "14", "20", "15", "15", "6", "1", "7", "7", "17", "7", "18", "18", "23", "7", "19", "19" ]
[ "nonn", "look", "base" ]
30
0
4
[ "A000079", "A000120", "A057168", "A068076", "A263017", "A361079" ]
null
Alois P. Heinz, Mar 01 2023
2023-03-16T04:52:41
oeisdata/seq/A361/A361079.seq
cde4fcee5ac26f230f7a504e3d4dacad
A361080
Numbers that set records in A360224.
[ "1", "12", "18", "28", "30", "38", "42", "48", "60", "72", "102", "108", "138", "150", "168", "180", "192", "228", "240", "270", "282", "312", "348", "402", "420", "432", "462", "522", "570", "600", "618", "642", "660", "732", "768", "798", "810", "858", "882", "990", "1008", "1020", "1050", "1092", "1152", "1218", "1230", "1278", "1290", "1320", "1428", "1452", "1482", "1608", "1620", "1722", "1788", "1830", "1848" ]
[ "nonn" ]
12
1
2
[ "A360224", "A361080", "A361081" ]
null
Michael De Vlieger, Jun 13 2023
2023-06-15T10:32:28
oeisdata/seq/A361/A361080.seq
6d858b3155ed51daca12bbde81cc5e03
A361081
Records in A360224.
[ "0", "1", "3", "4", "5", "6", "12", "14", "19", "31", "46", "52", "68", "70", "74", "89", "104", "123", "128", "146", "158", "176", "199", "207", "229", "257", "264", "311", "339", "370", "375", "391", "396", "409", "428", "446", "514", "532", "559", "578", "595", "650", "666", "695", "727", "728", "801", "807", "843", "861", "929", "939", "953", "1025", "1087", "1134", "1143", "1164", "1197", "1221", "1282", "1314", "1327" ]
[ "nonn" ]
14
1
3
[ "A360224", "A361080", "A361081" ]
null
Michael De Vlieger, Jun 13 2023
2024-07-28T03:47:59
oeisdata/seq/A361/A361081.seq
2d4bc820abe2e954b666f151789dd0c4
A361082
Number of 3 X 3 matrices with unit determinant and positive integer entries whose sum is n.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "9", "18", "72", "108", "234", "360", "747", "756", "1818", "1782", "3222", "3672", "6615", "5850", "11394", "11034", "16623", "17028", "30204", "22248", "45792", "39204", "56853", "57906", "87984", "72036", "128160", "108990", "154890" ]
[ "nonn" ]
13
0
12
[ "A000010", "A361082", "A361083" ]
null
M. F. Hasler, Mar 01 2023
2023-03-28T08:21:51
oeisdata/seq/A361/A361082.seq
c7aa8f7ec3c2c0462c74518ef3a277a7
A361083
Number of 3 X 3 matrices with unit determinant and nonnegative integer entries whose sum is n.
[ "0", "0", "0", "3", "18", "54", "126", "261", "432", "783", "1134", "1899", "2286", "3960", "4680", "6876", "8262", "12654", "12618", "20799", "20934", "30024", "32760", "48141", "43632", "68976", "68094", "91161", "93042", "138006", "112194", "187227", "170982", "224892", "226728", "310824", "265770", "418410", "372384", "484920", "455400" ]
[ "nonn" ]
36
0
4
[ "A000010", "A361082", "A361083" ]
null
M. F. Hasler, Mar 01 2023
2023-03-11T06:22:16
oeisdata/seq/A361/A361083.seq
06937beef68d3cd1b68dbe8bc6ff9150
A361084
Number of partitions of [n] such that in each block the smallest element and the largest element have opposite parities.
[ "1", "0", "1", "0", "3", "2", "17", "28", "171", "430", "2617", "8496", "54739", "214714", "1477153", "6743204", "49550011", "256645926", "2010328585", "11602635128", "96590823907", "612918061426", "5404902119025", "37319203169580", "347468152001739", "2589081441826334", "25375080898848729", "202668739104752960" ]
[ "nonn" ]
17
0
5
[ "A000110", "A059841", "A361084", "A363592" ]
null
Alois P. Heinz, Jun 12 2023
2023-06-12T14:54:21
oeisdata/seq/A361/A361084.seq
e6beb1b9f277e5d64cb3c85f2fe60bf9
A361085
Least prime p > prime(n) such that at least one of p * prime(n)# +- 1 is not squarefree, where prime(n)# is the n-th primorial A002110(n).
[ "3", "5", "29", "31", "139", "167", "43", "127", "211", "41", "607", "1223", "71", "769", "1549", "947", "269", "1129", "163", "577", "673", "107", "4057", "1979", "433", "3833", "4177", "383", "1723", "409", "2399", "4517", "3803", "3061", "3299", "457", "3779", "971", "5749", "2843", "13709" ]
[ "nonn", "hard", "more" ]
33
0
1
[ "A002110", "A007018", "A013929", "A228649", "A361085" ]
null
M. F. Hasler, Mar 28 2023
2023-04-01T23:27:28
oeisdata/seq/A361/A361085.seq
e78a675e7f512d07f2931f14f41ca152
A361086
a(n) = a(n-1)*(a(n-1)^2 - 1) with a(0) = 2.
[ "2", "6", "210", "9260790", "794226015149981778210", "500993769952171221242360491304282624082148055373236400176882790" ]
[ "nonn", "less" ]
34
0
1
[ "A002110", "A007018", "A228649", "A361085", "A361086" ]
null
M. F. Hasler, Mar 28 2023
2023-04-17T23:53:36
oeisdata/seq/A361/A361086.seq
7303e54b2cc2e5abfe33925c0274ba90
A361087
Maximum squared inverse distance from the origin to the hyperplane defined by hypercube points.
[ "1", "1", "3", "7", "19" ]
[ "nonn", "hard", "more" ]
21
1
3
null
null
Veit Elser, Jun 12 2023
2024-03-08T23:11:54
oeisdata/seq/A361/A361087.seq
8960f5e072caa99c9bc188c51abd00b9
A361088
Irregular table, read by rows, where row n holds the tau signature of n, i.e., the shortest sequence (tau(n+k), 0 <= k <= m) that uniquely identifies n; tau = A000005.
[ "1", "2", "2", "2", "3", "3", "2", "2", "4", "2", "4", "2", "4", "2", "4", "3", "4", "3", "3", "4", "2", "4", "2", "6", "2", "6", "2", "4", "6", "2", "4", "2", "4", "4", "5", "4", "4", "5", "4", "5", "5", "2", "2", "6", "2", "6", "6", "2", "6", "2", "6", "4", "4", "2", "6", "4", "4", "2", "8", "4", "4", "2", "8", "4", "2", "8", "2", "8", "3", "8", "3", "3", "4", "4", "6", "2", "4", "4", "6", "2", "8", "4", "6", "2", "8", "2", "6", "2", "8", "2", "6", "2", "8" ]
[ "nonn", "tabf" ]
23
1
2
[ "A000005", "A161460", "A309981", "A327265", "A361088" ]
null
M. F. Hasler, Apr 07 2023
2025-03-25T08:56:15
oeisdata/seq/A361/A361088.seq
1631de05f5c17fcf088ecff7602d1712
A361089
a(n) = smallest integer x such that Sum_{k = 2..x} 1/(k*log(log(k))) > n.
[ "3", "5", "8", "21", "76", "389", "2679", "23969", "269777", "3717613", "61326301", "1188642478", "26651213526", "682263659097", "19720607003199", "637490095320530", "22857266906194526", "902495758030572213", "38993221443197045348", "1833273720522384358862" ]
[ "nonn" ]
41
2
1
[ "A077761", "A086242", "A137245", "A138312", "A221711", "A303493", "A319231", "A319232", "A354887", "A354917", "A354952", "A361089", "A361972", "A362533", "A363078", "A363368" ]
null
Artur Jasinski, Jun 11 2023
2023-07-15T05:33:51
oeisdata/seq/A361/A361089.seq
b4b00f920b4f671efecbf33965b1eb9d
A361090
E.g.f. satisfies A(x) = exp( x/(1 - x/A(x)) ).
[ "1", "1", "3", "7", "-11", "-239", "-179", "24991", "192025", "-3955391", "-89483399", "552615031", "46231717621", "254468241457", "-26683006147979", "-571848064714289", "14926049610344881", "825004339886219521", "-2973711136010539535", "-1134313888244827421465", "-17734152216328857754739" ]
[ "sign" ]
14
0
3
[ "A161630", "A212722", "A212917", "A361067", "A361090", "A361091", "A361092", "A361095" ]
null
Seiichi Manyama, Mar 01 2023
2023-03-15T11:11:34
oeisdata/seq/A361/A361090.seq
25a444ceb0657be11fdb66ab9255c927
A361091
E.g.f. satisfies A(x) = exp( x/(1 - x/A(x)^2) ).
[ "1", "1", "3", "1", "-71", "-19", "10051", "12349", "-3185391", "-9346247", "1797304771", "9717361721", "-1582301193527", "-13722004186331", "2000705907453891", "25552516703201461", "-3432004488804778079", "-60960914621687232271", "7660860906885122096515" ]
[ "sign" ]
12
0
3
[ "A161630", "A212722", "A212917", "A361068", "A361090", "A361091", "A361092", "A361096" ]
null
Seiichi Manyama, Mar 01 2023
2023-03-14T13:42:56
oeisdata/seq/A361/A361091.seq
82d063bf4efd01260df88f5b8dc51ebe
A361092
E.g.f. satisfies A(x) = exp( x/(1 - x/A(x)^3) ).
[ "1", "1", "3", "-5", "-107", "1041", "20701", "-440033", "-8464455", "343190593", "5639857561", "-423764450889", "-4968055259771", "754544622295153", "3846355902999429", "-1818148417882379729", "6637679490204153841", "5658469355898945338625", "-84578525845602646639823" ]
[ "sign" ]
13
0
3
[ "A161630", "A212722", "A212917", "A361069", "A361090", "A361091", "A361092", "A361097" ]
null
Seiichi Manyama, Mar 01 2023
2023-03-14T13:43:38
oeisdata/seq/A361/A361092.seq
9a2fc7698589a58cb2ec417096437872
A361093
E.g.f. satisfies A(x) = exp( 1/(1 - x * A(x)^2) - 1 ).
[ "1", "1", "7", "97", "2049", "58541", "2114143", "92419965", "4746108769", "280105517881", "18683156508471", "1389960074426969", "114119472522112225", "10249863809271551973", "999746622121255094479", "105236583967331849218741", "11891012005206169120252737", "1435560112909007680593616625" ]
[ "nonn" ]
16
0
3
[ "A052873", "A212722", "A361065", "A361093", "A361094", "A361095", "A361096", "A361097" ]
null
Seiichi Manyama, Mar 01 2023
2023-03-16T02:48:57
oeisdata/seq/A361/A361093.seq
5271e9f4670aa0684d7586f0368975b0
A361094
E.g.f. satisfies A(x) = exp( 1/(1 - x * A(x)^3) - 1 ).
[ "1", "1", "9", "166", "4717", "182136", "8911549", "528571408", "36864033945", "2956595372416", "268116203622961", "27128338649300736", "3029974270053623941", "370289278173654092800", "49150116757136815109733", "7041536364582774222616576", "1083004122024520209576760369" ]
[ "nonn" ]
15
0
3
[ "A052873", "A212917", "A361066", "A361093", "A361094", "A361095", "A361096", "A361097" ]
null
Seiichi Manyama, Mar 01 2023
2023-03-14T03:42:00
oeisdata/seq/A361/A361094.seq
a3a053b27f41419358197214bbf0ed2f
A361095
E.g.f. satisfies A(x) = exp( 1/(1 - x/A(x)) - 1 ).
[ "1", "1", "1", "-2", "-3", "56", "-155", "-2736", "34489", "72064", "-6599799", "53676800", "1155350581", "-32238425088", "-3604716947", "14790925735936", "-235482791871375", "-4972572910452736", "254158358486634001", "-1028499606209101824", "-202204782754527137939", "5371925138905661440000" ]
[ "sign" ]
11
0
4
[ "A052873", "A361093", "A361094", "A361095", "A361096", "A361097" ]
null
Seiichi Manyama, Mar 01 2023
2023-03-15T11:11:31
oeisdata/seq/A361/A361095.seq
940b5f6277f5664f7dd6e7315e0221a7
A361096
E.g.f. satisfies A(x) = exp( 1/(1 - x/A(x)^2) - 1 ).
[ "1", "1", "-1", "1", "17", "-339", "4999", "-63587", "566145", "3549241", "-405637489", "15518099961", "-446235202799", "9617693853925", "-75522664207017", "-7341781870733099", "596513949276803969", "-30104875035438797583", "1144712508931072057375", "-27381639204739332379151" ]
[ "sign" ]
12
0
5
[ "A052873", "A361093", "A361094", "A361095", "A361096", "A361097" ]
null
Seiichi Manyama, Mar 01 2023
2023-03-15T11:11:37
oeisdata/seq/A361/A361096.seq
70d123230d7ee8415c5ea4f797b958c3
A361097
E.g.f. satisfies A(x) = exp( 1/(1 - x/A(x)^3) - 1 ).
[ "1", "1", "-3", "22", "-251", "3816", "-71207", "1542640", "-36997431", "929097856", "-22062115979", "334968255744", "13395424571725", "-2177817789105152", "201597999475333329", "-16622491076645341184", "1332634806870147259537", "-107073894723559010304000" ]
[ "sign" ]
11
0
3
[ "A052873", "A361093", "A361094", "A361095", "A361096", "A361097" ]
null
Seiichi Manyama, Mar 01 2023
2023-03-14T13:44:26
oeisdata/seq/A361/A361097.seq
e8ddf76ba617db712e6bfc8b04caee12
A361098
Intersection of A360765 and A360768.
[ "36", "48", "50", "54", "72", "75", "80", "96", "98", "100", "108", "112", "135", "144", "147", "160", "162", "189", "192", "196", "200", "216", "224", "225", "240", "242", "245", "250", "252", "270", "288", "294", "300", "320", "324", "336", "338", "350", "352", "360", "363", "375", "378", "384", "392", "396", "400", "405", "416", "432", "441", "448", "450", "468", "480", "484", "486", "490", "500", "504", "507", "525" ]
[ "nonn" ]
15
1
1
[ "A000005", "A000010", "A001694", "A002182", "A007947", "A045763", "A053669", "A095990", "A119288", "A126706", "A168263", "A243822", "A243823", "A286708", "A303606", "A355432", "A359280", "A360480", "A360543", "A361098", "A361235" ]
null
Michael De Vlieger, Mar 15 2023
2024-02-24T11:07:38
oeisdata/seq/A361/A361098.seq
37ce97de9936a09ecc01fa1634f627d4
A361099
a(n) = n + 2*binomial(n,2) + 3*binomial(n,3) + 4*binomial(n,4).
[ "0", "1", "4", "12", "32", "75", "156", "294", "512", "837", "1300", "1936", "2784", "3887", "5292", "7050", "9216", "11849", "15012", "18772", "23200", "28371", "34364", "41262", "49152", "58125", "68276", "79704", "92512", "106807", "122700", "140306", "159744", "181137", "204612", "230300", "258336", "288859", "322012", "357942", "396800", "438741" ]
[ "nonn", "easy" ]
22
0
3
[ "A000290", "A004320", "A361099" ]
null
Enrique Navarrete, Mar 01 2023
2024-06-10T08:49:38
oeisdata/seq/A361/A361099.seq
1d0697cfa19cc2929327254e1aa4820e
A361100
Decimal expansion of 2^(2^(2^(2^2))) = 2^^5.
[ "2", "0", "0", "3", "5", "2", "9", "9", "3", "0", "4", "0", "6", "8", "4", "6", "4", "6", "4", "9", "7", "9", "0", "7", "2", "3", "5", "1", "5", "6", "0", "2", "5", "5", "7", "5", "0", "4", "4", "7", "8", "2", "5", "4", "7", "5", "5", "6", "9", "7", "5", "1", "4", "1", "9", "2", "6", "5", "0", "1", "6", "9", "7", "3", "7", "1", "0", "8", "9", "4", "0", "5", "9", "5", "5", "6", "3", "1", "1", "4", "5", "3", "0", "8", "9", "5", "0" ]
[ "nonn", "cons", "easy", "fini", "full" ]
28
19,730
1
[ "A014221", "A085667", "A241291", "A241292", "A241293", "A241294", "A241295", "A241296", "A241297", "A241298", "A241299", "A243913", "A361100" ]
null
Marco Ripà, Mar 03 2023
2024-01-31T03:58:50
oeisdata/seq/A361/A361100.seq
e8789343bbc6191753ccf9e5863b9875