Datasets:
christopher
/
oeis

Dataset card Data Studio Files
xet
Community
2
sequence_id
stringlengths
7
7
sequence_name
stringlengths
4
573
sequence
listlengths
1
348
keywords
listlengths
1
8
score
int64
1
2.35k
offset_a
int64
-14,827
666,262,453B
offset_b
int64
0
635M
⌀
cross_references
listlengths
1
128
⌀
former_ids
listlengths
1
3
⌀
author
stringlengths
7
231
⌀
timestamp
timestamp[us]date
1999-12-11 03:00:00
2025-07-14 02:38:35
filename
stringlengths
29
29
hash
stringlengths
32
32
A363001
a(n) = denominator(R(n, n, 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", "2", "2", "3", "2", "15", "2", "105", "2", "315", "2", "3465", "2", "45045", "2", "9009", "2", "153153", "2", "14549535", "2", "14549535", "2", "19684665", "2", "1673196525", "2", "5019589575", "2", "145568097675", "2", "4512611027925", "2", "4512611027925", "2", "4512611027925", "2", "166966608033225", "2", "316824683175", "2", "6845630929362225" ]
[ "nonn", "frac" ]
9
0
2
[ "A362999", "A363000", "A363001" ]
null
Peter Luschny, May 12 2023
2023-05-12T15:57:34
oeisdata/seq/A363/A363001.seq
7e61330c1e44dd7e2f933a9e81ee318f
A363002
Number of positive nondecreasing integer sequences of length n whose Gilbreath transform is (1, 1, ..., 1).
[ "1", "1", "1", "2", "5", "17", "82", "573", "5839", "86921", "1890317", "60013894", "2778068147" ]
[ "nonn", "more" ]
14
0
4
[ "A080839", "A362451", "A363002", "A363003", "A363004", "A363005" ]
null
Pontus von Brömssen, May 13 2023
2023-05-14T02:10:10
oeisdata/seq/A363/A363002.seq
55e14302f199a6da20f51d8539c1074a
A363003
Number of integer sequences of length n whose Gilbreath transform is (1, 1, ..., 1).
[ "1", "1", "2", "6", "26", "166", "1562", "21614", "438594", "13032614", "566069882" ]
[ "nonn", "more" ]
9
0
3
[ "A080839", "A363002", "A363003", "A363004", "A363005" ]
null
Pontus von Brömssen, May 13 2023
2023-05-13T13:48:09
oeisdata/seq/A363/A363003.seq
44d06e49f0e7d70883aca092005e6eae
A363004
Number of sequences of n distinct positive integers whose Gilbreath transform is (1, 1, ..., 1).
[ "1", "1", "1", "1", "2", "7", "40", "355", "4819", "99242", "3049155", "138762035" ]
[ "nonn", "more" ]
5
0
5
[ "A080839", "A363002", "A363003", "A363004", "A363005" ]
null
Pontus von Brömssen, May 13 2023
2023-05-13T13:22:36
oeisdata/seq/A363/A363004.seq
2aee776dd7b699db7730819e4b1d3801
A363005
Number of sequences of n distinct integers whose Gilbreath transform is (1, 1, ..., 1).
[ "1", "1", "2", "4", "12", "56", "416", "4764", "84272", "2278740", "92890636", "5659487836" ]
[ "nonn", "more" ]
10
0
3
[ "A080839", "A363002", "A363003", "A363004", "A363005" ]
null
Pontus von Brömssen, May 13 2023
2023-05-13T13:49:40
oeisdata/seq/A363/A363005.seq
3e9f0ecd67b6a38cf880d47ec3f5ab48
A363006
a(n) = 1/((d-1)*n + 1)*Sum_{i=0..n} binomial((d - 1)*n+1, n-i) * binomial((d-1)*n+i, i), with d = 6.
[ "1", "2", "22", "342", "6202", "122762", "2571326", "56031470", "1257199154", "28849835538", "673953255142", "15973925161030", "383186776643946", "9285457458463770", "226959074854361742", "5588974707042304222", "138529985051020001634", "3453373395317346136610", "86526667346028323084726", "2177844556015530807952438" ]
[ "nonn" ]
72
0
2
[ "A006318", "A027307", "A144097", "A217364", "A260332", "A363006", "A363305", "A364195", "A364196" ]
null
Michael De Vlieger, May 16 2023
2024-01-10T16:33:08
oeisdata/seq/A363/A363006.seq
49dd9fcc0afcb573b04bd168311d900d
A363007
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. 1/(1 - f^k(x)), where f(x) = exp(x) - 1.
[ "1", "1", "1", "1", "1", "2", "1", "1", "3", "6", "1", "1", "4", "13", "24", "1", "1", "5", "23", "75", "120", "1", "1", "6", "36", "175", "541", "720", "1", "1", "7", "52", "342", "1662", "4683", "5040", "1", "1", "8", "71", "594", "4048", "18937", "47293", "40320", "1", "1", "9", "93", "949", "8444", "57437", "251729", "545835", "362880", "1", "1", "10", "118", "1425", "15775", "143783", "950512", "3824282", "7087261", "3628800" ]
[ "nonn", "tabl" ]
18
0
6
[ "A000142", "A000670", "A083355", "A099391", "A153278", "A351420", "A351429", "A363007", "A363008", "A363009", "A363010" ]
null
Seiichi Manyama, May 12 2023
2023-05-12T16:27:06
oeisdata/seq/A363/A363007.seq
a71244181930407be29337007f6ecf75
A363008
Expansion of e.g.f. 1/(2 - exp(exp(exp(exp(x) - 1) - 1) - 1)).
[ "1", "1", "6", "52", "594", "8444", "143783", "2854261", "64735570", "1651560175", "46814933977", "1459689346911", "49650414218071", "1829560770160335", "72603137881845927", "3086932915850946633", "139999909097319319787", "6746170002325663539844", "344199636595620793896784" ]
[ "nonn" ]
12
0
3
[ "A153278", "A351427", "A363007", "A363008" ]
null
Seiichi Manyama, May 12 2023
2023-05-12T15:03:50
oeisdata/seq/A363/A363008.seq
fafbf04238eec651c4d13e00fb3f1b34
A363009
Expansion of e.g.f. 1/(2 - exp(exp(exp(exp(exp(x) - 1) - 1) - 1) - 1)).
[ "1", "1", "7", "71", "949", "15775", "313920", "7279795", "192828745", "5744627550", "190131836270", "6921735519110", "274885665920198", "11826225289547024", "547926995688877245", "27199542114163170649", "1440220170795372833970", "81026116511855753816058" ]
[ "nonn" ]
12
0
3
[ "A153278", "A351428", "A363007", "A363009" ]
null
Seiichi Manyama, May 12 2023
2023-05-12T15:07:29
oeisdata/seq/A363/A363009.seq
d8a4b43d8f88e92f795d1aa7982d141f
A363010
a(n) = n! * [x^n] 1/(1 - f^n(x)), where f(x) = exp(x) - 1.
[ "1", "1", "4", "36", "594", "15775", "618838", "33757864", "2448904188", "228290728635", "26617527649365", "3797508644987398", "651082351708066303", "132130157056046918808", "31333332827346731906130", "8587011712002719806274022", "2693586800519167315881703732", "958983405298849163873718493941" ]
[ "nonn" ]
21
0
3
[ "A139383", "A153278", "A261280", "A346802", "A351433", "A363007", "A363010" ]
null
Seiichi Manyama, May 12 2023
2023-05-12T16:26:33
oeisdata/seq/A363/A363010.seq
0bca5caf5c35f729a9204f32e3acfca0
A363011
Indices of record highs in A362816.
[ "1", "3", "9", "57", "504", "3847", "41170" ]
[ "more", "sign" ]
11
1
2
[ "A362815", "A362816", "A363011" ]
null
Samuel Harkness, May 12 2023
2023-05-16T08:12:45
oeisdata/seq/A363/A363011.seq
444d38815ebd292753d7704eb82a7bd0
A363012
a(n) = Sum_{d|n} d*tau(d)*phi(d)*mu(n/d).
[ "1", "3", "11", "20", "39", "33", "83", "104", "150", "117", "219", "220", "311", "249", "429", "512", "543", "450", "683", "780", "913", "657", "1011", "1144", "1460", "933", "1782", "1660", "1623", "1287", "1859", "2432", "2409", "1629", "3237", "3000", "2663", "2049", "3421", "4056", "3279", "2739", "3611", "4380", "5850", "3033", "4323", "5632", "6090", "4380" ]
[ "easy", "nonn", "mult" ]
17
1
2
[ "A000005", "A000010", "A008683", "A359954", "A363012" ]
null
Wesley Ivan Hurt, May 12 2023
2023-05-17T11:13:55
oeisdata/seq/A363/A363012.seq
b50b9ffda546dd4c5f2783d0fa121d7e
A363013
a(n) is the number of prime factors (counted with multiplicity) of the n-th cubefull number (A036966).
[ "0", "3", "4", "3", "5", "6", "4", "3", "7", "6", "5", "8", "3", "7", "9", "4", "7", "6", "8", "6", "10", "8", "3", "9", "8", "7", "11", "7", "3", "4", "9", "6", "5", "6", "10", "9", "8", "12", "3", "7", "10", "7", "9", "8", "3", "11", "10", "9", "13", "6", "8", "7", "11", "6", "8", "10", "3", "12", "4", "11", "6", "10", "14", "5", "7", "10", "6", "7", "9", "9", "12", "7", "9", "11", "3", "8", "9", "13", "7", "4", "3" ]
[ "nonn" ]
13
1
2
[ "A001222", "A036966", "A072047", "A076399", "A360729", "A362974", "A363013" ]
null
Amiram Eldar, May 13 2023
2024-09-21T14:46:12
oeisdata/seq/A363/A363013.seq
3d593cd9e7f1fb59f4f4cf11e62cdbe1
A363014
Cubefull numbers (A036966) with a record gap to the next cubefull number.
[ "1", "8", "16", "32", "81", "128", "343", "512", "729", "864", "1024", "1331", "3456", "4096", "6912", "8192", "12167", "25000", "32768", "35937", "43904", "46656", "55296", "70304", "93312", "110592", "117649", "140608", "186624", "287496", "331776", "357911", "373248", "592704", "707281", "889056", "1000000", "1124864", "1157625", "1296000" ]
[ "nonn" ]
10
1
2
[ "A036966", "A349062", "A363014" ]
null
Amiram Eldar, May 13 2023
2023-05-13T06:17:22
oeisdata/seq/A363/A363014.seq
c8cf42eea868847c6b859611f04b84e8
A363015
Expansion of g.f. A(x) satisfying 3 = Sum_{n=-oo..+oo} x^n * A(x)^n * (1 + x^n)^(2*n+1).
[ "1", "0", "5", "13", "80", "352", "1955", "10155", "56934", "316413", "1810151", "10415443", "60776075", "357233548", "2118007035", "12637190038", "75866774437", "457815076217", "2775815358337", "16900781081347", "103294693694125", "633491925784696", "3897330320229845", "24045718580772438", "148748241343153325" ]
[ "nonn" ]
8
0
3
null
null
Paul D. Hanna, May 18 2023
2023-05-18T10:41:16
oeisdata/seq/A363/A363015.seq
2885a391c8402acf2bb41b0c945becc6
A363016
a(n) is the least integer k such that the k-th, (k+1)-th, ..., (k+n-1)-th primes are congruent to 1 mod 4.
[ "3", "6", "24", "77", "378", "1395", "1395", "1395", "1395", "31798", "61457", "240748", "800583", "804584", "804584", "804584", "16118548", "16138563", "16138563", "56307979", "56307979", "56307979", "56307979", "56307979", "3511121443", "3511121443", "26284355567", "26284355567", "26284355567", "118027458557", "118027458557", "118027458557", "118027458557" ]
[ "nonn" ]
26
1
1
[ "A000720", "A023512", "A057624", "A363016", "A363017" ]
null
Léo Gratien, May 13 2023
2023-05-16T08:13:23
oeisdata/seq/A363/A363016.seq
05d9b2f79dbc479d2391c39462752309
A363017
a(n) is the least integer k such that the k-th, (k+1)-th, ..., (k+n-1)-th primes are congruent to 3 mod 8.
[ "2", "94", "334", "4422", "23969", "303493", "303493", "606529", "28725046", "92865581", "397316305", "511883558", "848516256", "23738949809", "144899085865", "469694200388", "3800553021301", "8571139291304", "63858322306341", "90990757864814" ]
[ "nonn", "more" ]
28
1
1
[ "A023512", "A057632", "A363016", "A363017" ]
null
Léo Gratien, May 13 2023
2023-05-28T15:40:45
oeisdata/seq/A363/A363017.seq
1dcb402280b1aed4d1f283e5e4622e75
A363018
Decimal expansion of Product_{k>=1} (1 - exp(-6*Pi*k)).
[ "9", "9", "9", "9", "9", "9", "9", "9", "3", "4", "8", "7", "5", "8", "7", "8", "2", "1", "5", "0", "8", "5", "8", "7", "4", "4", "1", "6", "2", "7", "0", "6", "1", "2", "4", "3", "1", "0", "8", "3", "3", "0", "5", "0", "8", "1", "3", "6", "0", "9", "7", "2", "3", "6", "6", "2", "0", "8", "7", "0", "2", "3", "9", "0", "6", "6", "2", "3", "9", "9", "5", "9", "4", "1", "5", "9", "1", "8", "8", "8", "6", "5", "1", "9", "7", "6", "6", "3", "5", "5", "9", "6", "5", "6", "8", "6", "9", "2", "9", "8", "1", "8", "2", "8", "4", "1" ]
[ "nonn", "cons" ]
17
0
1
[ "A259148", "A259149", "A259150", "A259151", "A292864", "A292888", "A292905", "A363018", "A363019", "A363020", "A363021", "A363081", "A363117", "A363118", "A363119", "A363120", "A363178", "A363179" ]
null
Vaclav Kotesovec, May 13 2023
2023-05-19T14:30:52
oeisdata/seq/A363/A363018.seq
50dfeb84c5a48287e414cc9cf58d05e1
A363019
Decimal expansion of Product_{k>=1} (1 - exp(-10*Pi*k)).
[ "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "7", "7", "2", "8", "8", "9", "8", "9", "3", "1", "6", "7", "5", "8", "5", "4", "5", "8", "2", "3", "2", "0", "0", "9", "9", "3", "3", "2", "5", "0", "2", "9", "4", "8", "2", "7", "0", "7", "0", "6", "7", "4", "1", "3", "2", "0", "5", "4", "5", "3", "3", "6", "2", "9", "9", "5", "3", "9", "3", "6", "4", "0", "1", "3", "8", "4", "1", "9", "7", "2", "4", "3", "0", "5", "3", "4", "8", "2", "3", "7", "3", "4", "5", "6", "9", "4", "5", "3", "8", "7", "7", "7", "0" ]
[ "nonn", "cons" ]
16
0
1
[ "A259148", "A259149", "A259150", "A259151", "A292864", "A292888", "A292905", "A363018", "A363019", "A363020", "A363021", "A363081", "A363117", "A363118", "A363119", "A363120", "A363178", "A363179" ]
null
Vaclav Kotesovec, May 13 2023
2023-05-19T14:31:48
oeisdata/seq/A363/A363019.seq
542fdc27042b2ed77958ef32767d5506
A363020
Decimal expansion of Product_{k>=1} (1 - exp(-12*Pi*k)).
[ "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "5", "7", "5", "8", "8", "4", "8", "8", "1", "6", "9", "8", "3", "9", "2", "2", "2", "7", "6", "1", "0", "8", "9", "0", "2", "0", "2", "2", "0", "5", "5", "9", "6", "6", "9", "3", "6", "2", "7", "2", "7", "6", "0", "8", "3", "7", "0", "5", "2", "5", "0", "3", "7", "2", "4", "8", "2", "7", "2", "4", "8", "8", "7", "7", "0", "1", "0", "8", "7", "3", "5", "5", "4", "7", "3", "8", "9", "0", "7", "7", "7", "2", "9", "6", "8", "0", "6", "1", "8", "0" ]
[ "nonn", "cons" ]
13
0
1
[ "A259148", "A259149", "A259150", "A259151", "A292864", "A292888", "A292905", "A363018", "A363019", "A363020", "A363021", "A363081", "A363117", "A363118", "A363119", "A363120", "A363178", "A363179" ]
null
Vaclav Kotesovec, May 13 2023
2023-05-19T14:32:15
oeisdata/seq/A363/A363020.seq
2beeae74b44d50b1fbe22c50d3a96921
A363021
Decimal expansion of Product_{k>=1} (1 - exp(-20*Pi*k)).
[ "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "4", "8", "4", "2", "0", "9", "9", "9", "3", "7", "4", "5", "7", "1", "5", "9", "6", "4", "9", "5", "8", "1", "5", "1", "9", "7", "7", "1", "1", "2", "7", "1", "1", "6", "2", "5", "1", "0", "2", "3", "6", "9", "0", "9", "9", "7", "4", "0", "3", "2", "0", "3", "2", "0", "0", "1", "4", "5", "0", "8", "1", "5", "0", "6", "5", "4", "3", "1", "7", "6", "9", "1", "7", "9", "9", "9", "4", "9", "7" ]
[ "nonn", "cons" ]
13
0
1
[ "A259148", "A259149", "A259150", "A259151", "A292864", "A292888", "A292905", "A363018", "A363019", "A363020", "A363021", "A363081", "A363117", "A363118", "A363119", "A363120", "A363178", "A363179" ]
null
Vaclav Kotesovec, May 13 2023
2023-05-19T14:33:01
oeisdata/seq/A363/A363021.seq
53db9bbd981e9df8a6842dd7d0105a98
A363022
Expansion of Sum_{k>0} x^(2*k)/(1+x^k)^3.
[ "0", "1", "-3", "7", "-10", "13", "-21", "35", "-39", "36", "-55", "85", "-78", "71", "-118", "155", "-136", "130", "-171", "232", "-234", "177", "-253", "389", "-310", "248", "-390", "455", "-406", "378", "-465", "651", "-586", "426", "-626", "832", "-666", "533", "-822", "1040", "-820", "734", "-903", "1129", "-1144", "783", "-1081", "1637", "-1197", "961", "-1414", "1580", "-1378" ]
[ "sign" ]
87
1
3
[ "A002129", "A069153", "A321543", "A325940", "A363022", "A363598", "A363613", "A363614" ]
null
Seiichi Manyama, Jun 11 2023
2023-07-25T17:29:18
oeisdata/seq/A363/A363022.seq
74d0899858226659a9a9789481f0103d
A363023
Primes composed of the digits 1, 6, and 9.
[ "11", "19", "61", "191", "199", "619", "661", "691", "911", "919", "991", "1619", "1669", "1699", "1999", "6199", "6619", "6661", "6691", "6911", "6961", "6991", "9161", "9199", "9619", "9661", "11119", "11161", "11699", "11969", "16111", "16619", "16661", "16691", "16699", "19661", "19699", "19919", "19961", "19991", "61169", "61961" ]
[ "nonn", "base" ]
11
1
1
[ "A020454", "A020457", "A363023" ]
null
Harvey P. Dale, May 13 2023
2023-05-13T14:12:29
oeisdata/seq/A363/A363023.seq
f887889891d43a6b9590dacbc6c61d7c
A363024
Primes of the form 3^(k-1) - 2^k.
[ "11", "179", "601", "1931", "10456158899", "617669101316651", "984770866999239144049", "2153693958571958138940251", "1570042898793851235488822819", "14130386090585813000157964091", "11972515182561981102976512358583456508049", "19088056323407826758511836230558252318494847619" ]
[ "nonn" ]
33
1
1
[ "A003063", "A162714", "A162715", "A363024", "A363375" ]
null
Sébastien Tao, May 13 2023
2023-06-04T21:12:20
oeisdata/seq/A363/A363024.seq
49f1f1e7cea2eab90dffa6915872389c
A363025
Sum of divisors of 5*n-2 of form 5*k+2.
[ "0", "2", "0", "2", "0", "9", "0", "2", "0", "14", "0", "2", "7", "19", "0", "2", "0", "24", "0", "9", "0", "41", "0", "2", "0", "34", "7", "2", "0", "39", "17", "2", "0", "63", "0", "2", "0", "49", "0", "24", "7", "54", "0", "2", "0", "71", "0", "26", "27", "64", "0", "2", "0", "69", "7", "2", "0", "118", "0", "2", "0", "108", "0", "2", "17", "84", "37", "2", "7", "101", "0", "2", "0", "94", "0", "78", "0", "99", "0", "2", "0", "133", "7", "24", "47", "109", "0", "2", "0", "153", "0" ]
[ "nonn" ]
16
1
2
[ "A284280", "A359269", "A362952", "A363025", "A363026", "A363027", "A363029" ]
null
Seiichi Manyama, Jul 06 2023
2023-07-06T07:29:20
oeisdata/seq/A363/A363025.seq
71d686989fa19e52943e942df1c9a7f0
A363026
Sum of divisors of 5*n-3 of form 5*k+2.
[ "2", "7", "14", "17", "24", "27", "34", "37", "51", "47", "54", "57", "64", "67", "86", "84", "84", "87", "94", "97", "121", "107", "121", "117", "124", "127", "168", "137", "144", "154", "154", "157", "191", "167", "174", "177", "191", "204", "238", "197", "204", "207", "214", "224", "261", "227", "234", "237", "266", "247", "315", "257", "264", "267", "291", "277", "331", "294", "294", "324", "304", "307", "378", "317", "331", "327" ]
[ "nonn" ]
14
1
1
[ "A284280", "A359237", "A362952", "A363025", "A363026", "A363027", "A363030" ]
null
Seiichi Manyama, Jul 06 2023
2023-07-06T07:29:28
oeisdata/seq/A363/A363026.seq
9d4be5bb6fac312cda3a16e7ec7c6db2
A363027
Sum of divisors of 5*n-4 of form 5*k+2.
[ "0", "2", "0", "2", "7", "2", "0", "14", "0", "2", "17", "9", "0", "24", "0", "2", "27", "2", "7", "46", "0", "2", "37", "2", "0", "51", "0", "19", "47", "2", "0", "66", "7", "2", "57", "24", "0", "64", "0", "9", "67", "2", "0", "113", "17", "2", "84", "2", "0", "84", "0", "34", "87", "9", "0", "106", "0", "24", "97", "39", "7", "121", "0", "2", "107", "2", "0", "175", "0", "2", "144", "2", "0", "124", "7", "49", "127", "2", "17", "168", "0", "9", "137", "86", "0", "144", "0", "2" ]
[ "nonn", "look" ]
24
1
2
[ "A284280", "A359244", "A362952", "A363025", "A363026", "A363027", "A363032" ]
null
Seiichi Manyama, Jul 06 2023
2025-02-01T17:51:23
oeisdata/seq/A363/A363027.seq
17803f086dc22b9b8763d3e0307e59c2
A363028
Expansion of Sum_{k>0} k * x^(2*k-1) / (1 - x^(5*k-3)).
[ "1", "0", "3", "0", "4", "0", "5", "0", "6", "2", "7", "0", "8", "0", "9", "0", "15", "0", "11", "0", "12", "0", "13", "6", "14", "0", "15", "0", "19", "0", "24", "0", "18", "0", "19", "0", "20", "8", "21", "0", "29", "0", "23", "0", "33", "0", "25", "0", "26", "0", "27", "10", "36", "0", "29", "0", "30", "4", "42", "0", "32", "0", "33", "0", "43", "12", "35", "0", "36", "0", "37", "0", "51", "0", "48", "0", "50", "0", "41", "14", "42", "0", "43", "0", "44", "0", "60", "0" ]
[ "nonn" ]
19
1
3
[ "A359287", "A362952", "A363028", "A363155", "A364096", "A364104" ]
null
Seiichi Manyama, Jul 06 2023
2023-07-07T06:38:18
oeisdata/seq/A363/A363028.seq
8f68cd0aa67690ba9a7c97118ad2f0d0
A363029
Expansion of Sum_{k>0} k * x^(4*k-2) / (1 - x^(5*k-3)).
[ "0", "1", "0", "1", "0", "3", "0", "1", "0", "4", "0", "1", "2", "5", "0", "1", "0", "6", "0", "3", "0", "10", "0", "1", "0", "8", "2", "1", "0", "9", "4", "1", "0", "15", "0", "1", "0", "11", "0", "6", "2", "12", "0", "1", "0", "16", "0", "7", "6", "14", "0", "1", "0", "15", "2", "1", "0", "26", "0", "1", "0", "24", "0", "1", "4", "18", "8", "1", "2", "22", "0", "1", "0", "20", "0", "18", "0", "21", "0", "1", "0", "29", "2", "6", "10", "23", "0", "1", "0", "33", "0", "1", "0" ]
[ "nonn" ]
15
1
6
[ "A359269", "A363025", "A363029" ]
null
Seiichi Manyama, Jul 06 2023
2023-07-06T07:29:54
oeisdata/seq/A363/A363029.seq
efbe73b24a7fa378021543058e2e9733
A363030
Expansion of Sum_{k>0} k * x^k / (1 - x^(5*k-3)).
[ "1", "2", "4", "4", "6", "6", "8", "8", "12", "10", "12", "12", "14", "14", "19", "18", "18", "18", "20", "20", "26", "22", "26", "24", "26", "26", "36", "28", "30", "32", "32", "32", "40", "34", "36", "36", "40", "42", "50", "40", "42", "42", "44", "46", "54", "46", "48", "48", "55", "50", "66", "52", "54", "54", "60", "56", "68", "60", "60", "66", "62", "62", "78", "64", "68", "66", "68", "68", "82", "70", "84", "78", "74", "74", "92", "76", "78" ]
[ "nonn" ]
14
1
2
[ "A359237", "A363026", "A363030" ]
null
Seiichi Manyama, Jul 06 2023
2023-07-06T07:30:02
oeisdata/seq/A363/A363030.seq
a441878ee7eaee274d3b85e71b98ebfc
A363031
a(n) = sigma(6*n+1). Sum of the divisors of 6*n+1, n >= 0.
[ "1", "8", "14", "20", "31", "32", "38", "44", "57", "72", "62", "68", "74", "80", "108", "112", "98", "104", "110", "144", "133", "128", "160", "140", "180", "152", "158", "164", "183", "248", "182", "216", "194", "200", "252", "212", "256", "224", "230", "288", "242", "280", "288", "304", "324", "272", "278", "284", "307", "360", "352", "308", "314", "360", "434", "332", "338", "400", "350", "432", "381", "368", "374", "380", "576", "432" ]
[ "nonn", "easy" ]
34
0
2
[ "A000203", "A016921", "A224613", "A363031", "A363161" ]
null
Omar E. Pol, May 18 2023
2023-09-07T12:47:59
oeisdata/seq/A363/A363031.seq
b02afbcb1e5052944e2e6c8cb2d02ca8
A363032
Expansion of Sum_{k>0} k * x^(3*k-1) / (1 - x^(5*k-3)).
[ "0", "1", "0", "1", "2", "1", "0", "4", "0", "1", "4", "3", "0", "6", "0", "1", "6", "1", "2", "11", "0", "1", "8", "1", "0", "12", "0", "5", "10", "1", "0", "15", "2", "1", "12", "6", "0", "14", "0", "3", "14", "1", "0", "25", "4", "1", "18", "1", "0", "18", "0", "8", "18", "3", "0", "23", "0", "6", "20", "9", "2", "26", "0", "1", "22", "1", "0", "38", "0", "1", "30", "1", "0", "26", "2", "11", "26", "1", "4", "36", "0", "3", "28", "19", "0", "30", "0", "1", "32", "1", "0", "47", "0" ]
[ "nonn" ]
12
1
5
[ "A359244", "A363027", "A363032" ]
null
Seiichi Manyama, Jul 06 2023
2023-07-06T07:30:10
oeisdata/seq/A363/A363032.seq
b0ebe4f966d03a24848dc5070d96c9de
A363033
Sum of divisors of 5*n-1 of form 5*k+3.
[ "0", "3", "0", "0", "11", "0", "0", "16", "0", "0", "21", "0", "8", "26", "0", "0", "31", "0", "0", "36", "21", "0", "41", "0", "0", "46", "0", "0", "77", "0", "0", "56", "0", "13", "61", "0", "31", "66", "0", "0", "71", "0", "0", "76", "36", "0", "112", "0", "0", "86", "0", "0", "132", "0", "0", "96", "0", "0", "101", "36", "46", "106", "0", "0", "129", "0", "0", "116", "51", "0", "121", "0", "41", "126", "0", "0", "187", "0", "0", "136", "0", "0", "182", "0", "61", "192", "0", "0" ]
[ "nonn" ]
15
1
2
[ "A284281", "A359288", "A363033", "A363034", "A363035", "A363053", "A363155" ]
null
Seiichi Manyama, Jul 06 2023
2023-07-06T07:28:15
oeisdata/seq/A363/A363033.seq
23bfd8020bd735228f9f7027e7237caa
A363034
Sum of divisors of 5*n-2 of form 5*k+3.
[ "3", "8", "13", "21", "23", "28", "36", "38", "43", "59", "53", "58", "66", "68", "73", "94", "83", "96", "96", "98", "103", "129", "113", "118", "126", "136", "133", "164", "156", "148", "156", "158", "163", "207", "173", "178", "186", "188", "193", "252", "203", "229", "216", "218", "223", "269", "233", "238", "246", "256", "276", "304", "263", "268", "289", "278", "283", "365", "293", "298", "306", "336", "313", "374", "323" ]
[ "nonn" ]
15
1
1
[ "A284281", "A359236", "A363033", "A363034", "A363035", "A363053", "A363156" ]
null
Seiichi Manyama, Jul 06 2023
2023-07-06T07:30:17
oeisdata/seq/A363/A363034.seq
6ddeac2e304c3d726e3b5af3226ed0fd
A363035
Sum of divisors of 5*n-3 of form 5*k+3.
[ "0", "0", "3", "0", "0", "3", "8", "0", "3", "0", "13", "3", "0", "0", "29", "0", "0", "3", "23", "0", "3", "0", "36", "16", "0", "0", "36", "0", "0", "3", "46", "0", "21", "0", "43", "3", "13", "0", "59", "0", "0", "26", "53", "0", "3", "0", "66", "3", "0", "13", "112", "0", "0", "3", "76", "0", "3", "0", "73", "36", "0", "0", "102", "0", "23", "3", "83", "0", "59", "0", "96", "3", "0", "0", "96", "13", "0", "46", "134", "0", "3", "0", "103", "3", "0", "0", "185", "23", "13", "3", "113", "0", "36" ]
[ "nonn" ]
16
1
3
[ "A284281", "A359270", "A363033", "A363034", "A363035", "A363053", "A363157" ]
null
Seiichi Manyama, Jul 06 2023
2023-07-06T07:30:28
oeisdata/seq/A363/A363035.seq
0bf159597d719ac07f44284a52177b3b
A363036
Triangular array read by rows. T(n,k) is the number of regular elements in the semigroup of all binary relations on [n] that have rank k, n>=0, 0<=k<=n.
[ "1", "1", "1", "1", "9", "6", "1", "49", "306", "114", "1", "225", "8550", "26376", "5256", "1", "961", "194850", "3311250", "4669200", "507720" ]
[ "nonn", "tabl", "more" ]
27
0
5
[ "A003425", "A060867", "A354279", "A354741", "A363036" ]
null
Geoffrey Critzer, May 17 2023
2023-05-18T10:41:37
oeisdata/seq/A363/A363036.seq
55e1679bb0cb17c08d733a7627443522
A363037
Expansion of Sum_{k>0} x^k / (1 + x^(4*k)).
[ "1", "1", "1", "1", "0", "1", "1", "1", "2", "0", "1", "1", "0", "1", "0", "1", "2", "2", "1", "0", "0", "1", "1", "1", "1", "0", "2", "1", "0", "0", "1", "1", "2", "2", "0", "2", "0", "1", "0", "0", "2", "0", "1", "1", "0", "1", "1", "1", "2", "1", "2", "0", "0", "2", "0", "1", "2", "0", "1", "0", "0", "1", "1", "1", "0", "2", "1", "2", "0", "0", "1", "2", "2", "0", "1", "1", "0", "0", "1", "0", "3", "2", "1", "0", "0", "1", "0", "1", "2", "0", "0", "1", "0", "1", "0", "1", "2", "2", "3", "1", "0", "2", "1", "0", "0" ]
[ "nonn" ]
25
1
9
[ "A002654", "A363037", "A364011", "A364031", "A364032" ]
null
Seiichi Manyama, Jul 01 2023
2023-07-03T00:53:14
oeisdata/seq/A363/A363037.seq
19243c2d8572a4414899e798b6c665df
A363038
The decimal digits of a(n) correspond to the Gilbreath transform of the decimal digits of n.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "11", "10", "11", "12", "13", "14", "15", "16", "17", "18", "22", "21", "20", "21", "22", "23", "24", "25", "26", "27", "33", "32", "31", "30", "31", "32", "33", "34", "35", "36", "44", "43", "42", "41", "40", "41", "42", "43", "44", "45", "55", "54", "53", "52", "51", "50", "51", "52", "53", "54", "66", "65", "64", "63", "62", "61", "60", "61" ]
[ "nonn", "base", "easy" ]
13
0
3
[ "A000030", "A055642", "A334727", "A363038" ]
null
Rémy Sigrist, May 14 2023
2023-05-20T13:39:56
oeisdata/seq/A363/A363038.seq
2dc3bb4670c9898b9ee9c9b17f15a5f9
A363039
a(n) is the smallest tribonacci number (A000073) with exactly n divisors, or -1 if no such number exists.
[ "1", "2", "4", "274", "81", "44" ]
[ "sign", "more" ]
23
1
2
[ "A000005", "A000073", "A005179", "A081979", "A363039" ]
null
Ilya Gutkovskiy, May 14 2023
2025-02-16T08:34:05
oeisdata/seq/A363/A363039.seq
065b4c3a429b358445ca698394e6310a
A363040
a(n) is the smallest number which can be represented as the sum of n distinct perfect powers (A001597) in exactly n ways, or -1 if no such number exists.
[ "1", "17", "37", "53", "86", "119", "177", "215", "275", "331", "424", "516", "632", "764", "928", "1057", "1247", "1427", "1635", "1879", "2119", "2409", "2715", "3008", "3395", "3760", "4189", "4667", "5171", "5617", "6178", "6786", "7438", "8071", "8836", "9572", "10456", "11333", "12396", "13266", "14214", "15379", "16518", "17703", "19018", "20275" ]
[ "nonn" ]
12
1
2
[ "A001597", "A362424", "A362425", "A362428", "A363040" ]
null
Ilya Gutkovskiy, May 14 2023
2025-02-16T08:34:05
oeisdata/seq/A363/A363040.seq
8e8512c661659b60e456c48751e02d26
A363041
Triangle read by rows: T(n,k) = Stirling2(n+1,k)/binomial(k+1,2) if n-k is even, else 0 (1 <= k <= n).
[ "1", "0", "1", "1", "0", "1", "0", "5", "0", "1", "1", "0", "15", "0", "1", "0", "21", "0", "35", "0", "1", "1", "0", "161", "0", "70", "0", "1", "0", "85", "0", "777", "0", "126", "0", "1", "1", "0", "1555", "0", "2835", "0", "210", "0", "1", "0", "341", "0", "14575", "0", "8547", "0", "330", "0", "1", "1", "0", "14421", "0", "91960", "0", "22407", "0", "495", "0", "1" ]
[ "nonn", "tabl", "easy" ]
26
1
8
[ "A008275", "A008277", "A129825", "A164652", "A363041", "A363042" ]
null
Peter Bala, May 14 2023
2023-05-23T08:17:48
oeisdata/seq/A363/A363041.seq
81755541572bdb61d321e3cea7a0c70d
A363042
Row sums of A363041.
[ "1", "1", "2", "6", "17", "57", "233", "989", "4602", "23794", "129285", "751973", "4680041", "30523105", "210159654", "1521122754", "11481486845", "90604333205", "744420806913", "6348340033789", "56202980961206", "514994183598470", "4877587872447801", "47711923353493817", "481072714151555073", "4995769099914083313" ]
[ "nonn", "easy" ]
9
1
3
[ "A008277", "A363041", "A363042" ]
null
Peter Bala, May 14 2023
2023-05-23T08:17:44
oeisdata/seq/A363/A363042.seq
43a3d42a791ecaa6b3d27c231fb41461
A363043
Triangle read by rows: T(n,k) is the number of unlabeled graphs with n nodes and packing chromatic number k, 1 <= k <= n.
[ "1", "1", "1", "1", "2", "1", "1", "4", "5", "1", "1", "6", "15", "11", "1", "1", "10", "42", "73", "29", "1", "1", "14", "109", "390", "439", "90", "1", "1", "21", "278", "1953", "5546", "4188", "358", "1", "1", "29", "687", "9085", "61023", "134183", "67888", "1771", "1", "1", "41", "1694", "40344", "572235", "3517101", "5860434", "2001582", "11735", "1" ]
[ "nonn", "tabl" ]
5
1
5
[ "A000041", "A000088", "A084268", "A275622", "A335203", "A362580", "A363043", "A363044" ]
null
Pontus von Brömssen, May 14 2023
2023-05-14T11:41:27
oeisdata/seq/A363/A363043.seq
ac6a96755ff965dc3c988908520e7ccf
A363044
Triangle read by rows: T(n,k) is the number of unlabeled connected graphs with n nodes and packing chromatic number k, 1 <= k <= n.
[ "1", "0", "1", "0", "1", "1", "0", "1", "4", "1", "0", "1", "9", "10", "1", "0", "1", "21", "61", "28", "1", "0", "1", "48", "305", "409", "89", "1", "0", "1", "109", "1475", "5077", "4097", "357", "1", "0", "1", "247", "6623", "55005", "129904", "67529", "1770", "1", "0", "1", "564", "28540", "505098", "3378636", "5792187", "1999810", "11734", "1" ]
[ "nonn", "tabl" ]
4
1
9
[ "A001349", "A084269", "A363043", "A363044" ]
null
Pontus von Brömssen, May 14 2023
2023-05-14T11:41:47
oeisdata/seq/A363/A363044.seq
632b8a9a74077ed59bd55d4ac1d7958b
A363045
Number of partitions of n whose greatest part is a multiple of 3.
[ "1", "0", "0", "1", "1", "2", "4", "5", "7", "11", "14", "19", "27", "34", "45", "60", "77", "99", "130", "163", "208", "265", "333", "417", "526", "651", "810", "1004", "1237", "1519", "1869", "2278", "2780", "3382", "4101", "4958", "5995", "7210", "8669", "10398", "12444", "14859", "17730", "21086", "25057", "29718", "35186", "41584", "49100", "57842", "68075", "79991" ]
[ "nonn" ]
29
0
6
[ "A038499", "A072233", "A363045", "A363048" ]
null
Seiichi Manyama, May 14 2023
2023-10-23T04:33:48
oeisdata/seq/A363/A363045.seq
3a1f2db38a27bd12b6f2b39f7a201c8c
A363046
Number of partitions of n whose greatest part is a multiple of 4.
[ "1", "0", "0", "0", "1", "1", "2", "3", "6", "7", "11", "14", "21", "26", "36", "45", "62", "76", "100", "124", "162", "199", "255", "314", "399", "488", "612", "748", "932", "1134", "1400", "1699", "2086", "2520", "3072", "3700", "4488", "5384", "6494", "7766", "9326", "11112", "13283", "15778", "18788", "22245", "26386", "31150", "36825", "43345", "51070", "59953" ]
[ "nonn" ]
19
0
7
[ "A363046", "A363048" ]
null
Seiichi Manyama, May 14 2023
2023-05-21T10:50:55
oeisdata/seq/A363/A363046.seq
6fe7ee9031a65c444f93178b2c62da47
A363047
Number of partitions of n whose greatest part is a multiple of 5.
[ "1", "0", "0", "0", "0", "1", "1", "2", "3", "5", "8", "11", "15", "21", "28", "38", "49", "64", "82", "105", "134", "168", "211", "263", "327", "406", "501", "616", "757", "926", "1133", "1378", "1676", "2031", "2460", "2970", "3581", "4306", "5173", "6197", "7419", "8855", "10561", "12565", "14934", "17712", "20982", "24805", "29294", "34529", "40658", "47785", "56104" ]
[ "nonn" ]
18
0
8
[ "A363047", "A363048" ]
null
Seiichi Manyama, May 14 2023
2023-05-21T10:51:40
oeisdata/seq/A363/A363047.seq
473edbe13b1d80109abfc8998ad899c5
A363048
Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows, where T(n,k) is the number of partitions of n whose greatest part is a multiple of k.
[ "1", "0", "1", "0", "2", "1", "0", "3", "1", "1", "0", "5", "3", "1", "1", "0", "7", "3", "2", "1", "1", "0", "11", "6", "4", "2", "1", "1", "0", "15", "7", "5", "3", "2", "1", "1", "0", "22", "12", "7", "6", "3", "2", "1", "1", "0", "30", "14", "11", "7", "5", "3", "2", "1", "1", "0", "42", "22", "14", "11", "8", "5", "3", "2", "1", "1", "0", "56", "27", "19", "14", "11", "7", "5", "3", "2", "1", "1", "0", "77", "40", "27", "21", "15", "12", "7", "5", "3", "2", "1", "1" ]
[ "nonn", "tabl" ]
42
0
5
[ "A000007", "A000041", "A008284", "A027187", "A052810", "A072233", "A323433", "A350890", "A363045", "A363046", "A363047", "A363048" ]
null
Seiichi Manyama, May 14 2023
2023-10-20T06:45:15
oeisdata/seq/A363/A363048.seq
22186eea35b56a56e8f37701150f1d5d
A363049
Even numbers k having fewer prime factors, counted with multiplicity, than k-1.
[ "46", "82", "106", "118", "166", "190", "226", "244", "262", "274", "298", "316", "326", "334", "346", "358", "386", "406", "442", "466", "478", "514", "526", "562", "568", "586", "622", "626", "676", "694", "706", "730", "766", "778", "802", "826", "838", "862", "886", "892", "898", "926", "946", "958", "982", "1006", "1018", "1030", "1046", "1054", "1090" ]
[ "nonn" ]
34
1
1
[ "A001222", "A339910", "A363049" ]
null
Alexandre Herrera, May 14 2023
2023-05-16T08:14:14
oeisdata/seq/A363/A363049.seq
19f9a9707069eb7c00c47f489f772e89
A363050
Lesser of two consecutive integers such that one has more prime factors (counted with multiplicity), but the other has more divisors.
[ "495", "728", "729", "975", "1071", "1424", "1616", "1700", "1862", "1875", "2024", "2144", "2223", "2349", "2384", "2415", "2624", "2996", "3104", "3124", "3125", "3159", "3184", "3483", "3663", "4095", "4130", "4292", "4304", "4335", "4779", "4976", "5103", "5312", "5427", "5535", "5589", "5624", "5775", "6224", "6416", "6544", "6560", "6704" ]
[ "nonn" ]
9
1
1
[ "A000005", "A001222", "A363050" ]
null
Jon E. Schoenfield, May 14 2023
2023-05-14T23:47:27
oeisdata/seq/A363/A363050.seq
e02f00b9bd20997962a7a3e74a8bcccb
A363051
a(n) = Sum_{b=0..floor(sqrt(n/2)), n-b^2 is square} b.
[ "0", "1", "0", "0", "1", "0", "0", "2", "0", "1", "0", "0", "2", "0", "0", "0", "1", "3", "0", "2", "0", "0", "0", "0", "3", "1", "0", "0", "2", "0", "0", "4", "0", "3", "0", "0", "1", "0", "0", "2", "4", "0", "0", "0", "3", "0", "0", "0", "0", "6", "0", "4", "2", "0", "0", "0", "0", "3", "0", "0", "5", "0", "0", "0", "5", "0", "0", "2", "0", "0", "0", "6", "3", "5", "0", "0", "0", "0", "0", "4", "0", "1", "0" ]
[ "nonn" ]
16
1
8
[ "A001481", "A022544", "A362961", "A363051" ]
null
Darío Clavijo, May 14 2023
2024-01-31T07:41:43
oeisdata/seq/A363/A363051.seq
95bc38613d2efcc561ed21da525104ce
A363052
Integers m for which there exist positive integers j, k such that j*k*(j+k) = m^2.
[ "4", "18", "24", "32", "36", "50", "60", "108", "140", "144", "150", "192", "252", "256", "288", "300", "360", "392", "400", "480", "486", "500", "540", "588", "648", "780", "816", "864", "882", "900", "972", "1008", "1014", "1050", "1120", "1152", "1156", "1176", "1200", "1350", "1372", "1452", "1536", "1620", "1764", "1800", "1848", "2016", "2040", "2048", "2178" ]
[ "nonn", "easy" ]
27
1
1
[ "A088915", "A363052" ]
null
Zhining Yang, May 15 2023
2023-07-03T12:20:37
oeisdata/seq/A363/A363052.seq
ead1de19bf18a9154cb544a275a60bdd
A363053
Sum of divisors of 5*n-4 of form 5*k+3.
[ "0", "3", "0", "8", "3", "13", "0", "21", "0", "23", "3", "36", "0", "36", "0", "38", "3", "43", "13", "59", "0", "53", "3", "58", "0", "84", "0", "76", "3", "73", "0", "94", "23", "83", "3", "96", "0", "96", "0", "126", "3", "103", "0", "137", "13", "113", "36", "118", "0", "126", "0", "136", "3", "171", "0", "164", "0", "156", "3", "156", "43", "174", "0", "158", "3", "163", "0", "255", "0", "173", "16", "178", "0", "186", "53", "196", "3", "193", "23", "252" ]
[ "nonn" ]
30
1
2
[ "A284281", "A359244", "A363033", "A363034", "A363035", "A363053", "A363158" ]
null
Seiichi Manyama, Jul 06 2023
2023-07-06T07:30:36
oeisdata/seq/A363/A363053.seq
9096ab7ec34182e587a46587a5029cb3
A363054
Look and say sequence: describe the previous term (method A, starting with 20).
[ "20", "1210", "11121110", "31123110", "132112132110", "11131221121113122110", "311311222112311311222110", "1321132132211213211321322110", "11131221131211132221121113122113121113222110", "3113112221131112311332211231131122211311123113322110" ]
[ "nonn", "base" ]
44
1
1
[ "A001140", "A001141", "A001143", "A001145", "A001151", "A001155", "A001387", "A005150", "A006715", "A006751", "A007651", "A045918", "A098595", "A363054" ]
null
Julia Zimmerman, May 15 2023
2024-12-20T10:59:14
oeisdata/seq/A363/A363054.seq
1f10c89890124501e23449d381b40d1f
A363055
Graph bandwidth of the n-Apollonian network.
[ "3", "4", "7", "16", "37" ]
[ "nonn", "more" ]
7
1
1
null
null
Eric W. Weisstein, May 15 2023
2025-02-16T08:34:05
oeisdata/seq/A363/A363055.seq
9b58729df7941808a1d6e96a6b997278
A363056
Graph bandwidth of the n X n queen graph.
[ "1", "3", "6", "11", "18", "25", "35" ]
[ "nonn", "more" ]
10
1
2
null
null
Eric W. Weisstein, May 15 2023
2025-02-16T08:34:05
oeisdata/seq/A363/A363056.seq
e2591bf2de7ade725460444fcb8723f3
A363057
Run lengths of the Fibonacci word (A003849).
[ "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2" ]
[ "nonn" ]
31
1
3
[ "A003849", "A096270", "A363057" ]
null
Jeffrey Shallit, May 15 2023
2024-04-30T08:28:56
oeisdata/seq/A363/A363057.seq
fb1230c8435157c83ec6284cbd22641a
A363058
Number of ways to get n points in a bridge hand.
[ "1", "2", "3", "5", "5", "8", "9", "12", "13", "16", "17", "21", "21", "24", "25", "28", "27", "30", "29", "31", "29", "30", "27", "28", "25", "24", "21", "21", "17", "16", "13", "11", "8", "6", "3", "2", "1" ]
[ "nonn", "fini", "full" ]
29
1
2
[ "A309777", "A363058" ]
null
Jud McCranie, May 16 2023
2023-10-19T06:28:00
oeisdata/seq/A363/A363058.seq
e86b3302309bcc8321bad4ae9912453c
A363059
Numbers k such that the number of divisors of k^2 equals the number of divisors of phi(k), where phi is the Euler totient function.
[ "1", "5", "57", "74", "202", "292", "394", "514", "652", "1354", "2114", "2125", "3145", "3208", "3395", "3723", "3783", "4053", "4401", "5018", "5225", "5298", "5425", "5770", "6039", "6363", "6795", "6918", "7564", "7667", "7676", "7852", "7964", "8585", "9050", "9154", "10178", "10535", "10802", "10818", "10954", "11223", "12411", "13074", "13634" ]
[ "nonn" ]
9
1
2
[ "A000005", "A000010", "A048691", "A052291", "A062821", "A259021", "A363059" ]
null
Amiram Eldar, May 16 2023
2023-05-16T12:50:59
oeisdata/seq/A363/A363059.seq
026a4eabd0b72a1a49ccb5835b127e5c
A363060
Numbers k such that 5 is the first digit of 2^k.
[ "9", "19", "29", "39", "49", "59", "69", "102", "112", "122", "132", "142", "152", "162", "172", "195", "205", "215", "225", "235", "245", "255", "265", "298", "308", "318", "328", "338", "348", "358", "391", "401", "411", "421", "431", "441", "451", "461", "494", "504", "514", "524", "534", "544", "554", "587", "597", "607", "617", "627", "637", "647", "657", "680", "690" ]
[ "nonn", "base", "easy" ]
36
1
1
[ "A000079", "A008952", "A018856", "A067469", "A067497", "A097415", "A172404", "A330243", "A363060", "A367294", "A367295", "A367296" ]
null
Ctibor O. Zizka, May 16 2023
2023-11-13T10:01:34
oeisdata/seq/A363/A363060.seq
168b8344ed9a180cd2492d0a8461523a
A363061
Number of k <= P(n) such that rad(k) | P(n), where rad(n) = A007947(n) and P(n) = A002110(n).
[ "1", "2", "5", "18", "68", "283", "1161", "4843", "19985", "83074", "349670", "1456458", "6107257", "25547835", "106115655", "440396113", "1833079809", "7642924612", "31705433101", "131711607956", "546283729493", "2257462298234", "9339325821411", "38593708318690", "159600066415313", "661371515924516", "2736805917843710" ]
[ "nonn", "hard" ]
52
0
2
[ "A002110", "A007947", "A010846", "A363061" ]
null
Michael De Vlieger, Jun 16 2023
2023-07-09T02:43:42
oeisdata/seq/A363/A363061.seq
d049df48f23ca470d3a3645c7676c985
A363062
G.f. A(x) satisfies: A(x) = x - x^2 * exp(A(x) + A(x^2)/2 + A(x^3)/3 + A(x^4)/4 + ...).
[ "1", "-1", "-1", "0", "1", "1", "-1", "-2", "0", "4", "4", "-5", "-13", "-2", "26", "30", "-29", "-94", "-26", "189", "246", "-198", "-769", "-302", "1512", "2228", "-1372", "-6691", "-3425", "12672", "21046", "-9503", "-60776", "-38353", "109719", "205330", "-61001", "-567518", "-427145", "967914", "2045196", "-314417", "-5405209", "-4743873", "8625547" ]
[ "sign" ]
7
1
8
[ "A007562", "A045648", "A345235", "A363062" ]
null
Ilya Gutkovskiy, May 16 2023
2023-05-18T10:41:33
oeisdata/seq/A363/A363062.seq
3cc9eafe9da8a3afae7cd5ce4b121c5b
A363063
Positive integers k such that the largest power of p dividing k is larger than or equal to the largest power of q dividing k (i.e., A305720(k,p) >= A305720(k,q)) for all primes p and q with p < q.
[ "1", "2", "4", "8", "12", "16", "24", "32", "48", "64", "96", "128", "144", "192", "256", "288", "384", "512", "576", "720", "768", "864", "1024", "1152", "1440", "1536", "1728", "2048", "2304", "2880", "3072", "3456", "4096", "4320", "4608", "5760", "6144", "6912", "8192", "8640", "9216", "10368", "11520", "12288", "13824", "16384", "17280", "18432" ]
[ "nonn" ]
41
1
2
[ "A087980", "A181818", "A305720", "A347284", "A363063", "A363098", "A363122" ]
null
Pontus von Brömssen, May 16 2023
2025-05-27T14:57:45
oeisdata/seq/A363/A363063.seq
391032b301c83ccc7bf17c42f7dd8a57
A363064
Number of connected Laplacian integral graphs on n vertices.
[ "1", "1", "2", "5", "12", "37", "94", "280", "912", "3164", "8424" ]
[ "nonn", "hard", "more" ]
23
1
3
[ "A000669", "A001349", "A064731", "A363064", "A363065" ]
null
Nathaniel Johnston, May 16 2023
2025-06-27T17:29:06
oeisdata/seq/A363/A363064.seq
af4525e4b326b7328ae95624dff06954
A363065
Number of Laplacian integral graphs on n vertices.
[ "1", "2", "4", "10", "24", "70", "188", "553", "1721", "5716" ]
[ "nonn", "more" ]
14
1
2
[ "A000084", "A000088", "A077027", "A363064", "A363065" ]
null
Nathaniel Johnston, May 16 2023
2023-05-26T11:29:22
oeisdata/seq/A363/A363065.seq
c7f159d2ffdde195adce2f8ce0b48338
A363066
Number of partitions p of n such that (1/3)*max(p) is a part of p.
[ "1", "0", "0", "0", "1", "1", "2", "3", "5", "6", "9", "11", "16", "20", "27", "33", "45", "55", "72", "89", "116", "142", "181", "222", "281", "343", "429", "522", "649", "786", "967", "1168", "1429", "1719", "2088", "2504", "3026", "3615", "4345", "5174", "6192", "7349", "8755", "10360", "12297", "14507", "17154", "20182", "23788", "27910", "32790", "38374", "44955", "52480", "61307", "71402" ]
[ "nonn" ]
33
0
7
[ "A002865", "A008484", "A035295", "A237825", "A238479", "A363045", "A363066", "A363067", "A363068" ]
null
Seiichi Manyama, May 16 2023
2025-06-29T18:23:08
oeisdata/seq/A363/A363066.seq
4c7a9b152d500e211b6d7da1a1fac9d5
A363067
Number of partitions p of n such that (1/4)*max(p) is a part of p.
[ "1", "0", "0", "0", "0", "1", "1", "2", "3", "5", "7", "10", "13", "18", "23", "31", "39", "51", "64", "81", "102", "128", "159", "198", "245", "304", "374", "460", "563", "689", "841", "1023", "1242", "1505", "1819", "2195", "2642", "3173", "3804", "4551", "5435", "6477", "7707", "9151", "10850", "12843", "15175", "17902", "21089", "24802", "29132", "34164", "40012", "46796", "54663", "63766" ]
[ "nonn" ]
27
0
8
[ "A002865", "A035296", "A237826", "A238479", "A363046", "A363066", "A363067", "A363068" ]
null
Seiichi Manyama, May 16 2023
2025-06-19T02:31:09
oeisdata/seq/A363/A363067.seq
66902d63b1124922e319c871d0b07ae9
A363068
Number of partitions p of n such that (1/5)*max(p) is a part of p.
[ "1", "0", "0", "0", "0", "0", "1", "1", "2", "3", "5", "7", "11", "14", "20", "26", "35", "44", "59", "73", "94", "117", "148", "181", "228", "277", "344", "418", "514", "621", "762", "917", "1116", "1342", "1624", "1945", "2348", "2803", "3366", "4012", "4798", "5700", "6798", "8052", "9565", "11305", "13383", "15771", "18618", "21880", "25745", "30187", "35414", "41414", "48461", "56531", "65967" ]
[ "nonn" ]
28
0
9
[ "A002865", "A035297", "A035298", "A237827", "A238479", "A363047", "A363066", "A363067", "A363068" ]
null
Seiichi Manyama, May 16 2023
2025-06-19T03:13:56
oeisdata/seq/A363/A363068.seq
5517d41012bca6f32e74a1553390ad9a
A363069
Size of the largest subset of {1,2,...,n} such that no two elements sum to a perfect square.
[ "1", "1", "1", "2", "2", "3", "4", "4", "4", "4", "5", "5", "6", "6", "6", "7", "8", "8", "8", "8", "9", "9", "10", "10", "11", "11", "12", "12", "12", "13", "13", "13", "13", "14", "14", "14", "15", "15", "16", "16", "17", "17", "18", "18", "18", "19", "19", "19", "20", "20", "20", "20", "21", "21", "22", "22", "23", "23", "24", "24", "25", "25", "25", "25", "26", "26", "26", "26", "26", "27", "27" ]
[ "nonn" ]
22
1
4
[ "A100719", "A210380", "A363069" ]
null
Zachary DeStefano, May 16 2023
2023-05-20T23:16:28
oeisdata/seq/A363/A363069.seq
1c84683c5ed95f00b946302fced65673
A363070
Take the terms 0..n of the infinite Fibonacci word A003849, regard them as a number in Fibonacci base.
[ "0", "1", "2", "3", "6", "10", "17", "28", "45", "74", "120", "194", "315", "510", "826", "1337", "2163", "3501", "5665", "9167", "14833", "24000", "38834", "62835", "101669", "164505", "266175", "430681", "696857", "1127538", "1824396", "2951935", "4776331", "7728267", "12504599", "20232867", "32737467", "52970334", "85707802", "138678137", "224385940", "363064078" ]
[ "base", "nonn" ]
65
0
3
[ "A003849", "A005713", "A182028", "A189920", "A363070" ]
null
Gandhar Joshi, May 16 2023
2023-06-08T10:34:23
oeisdata/seq/A363/A363070.seq
e16ebcc16f2d5c75f10da2a3d72b4bed
A363071
Number of partitions of [n] into m blocks that are ordered with increasing least elements and where block j contains n+1-j (m in {0..ceiling(n/2)}, j in {1..m}).
[ "1", "1", "1", "2", "3", "6", "13", "31", "80", "222", "659", "2082", "6966", "24574", "91067", "353443", "1432909", "6054025", "26599192", "121295345", "573065538", "2800640187", "14137645933", "73619324824", "394979697320", "2180911872495", "12380240599262", "72181691321844", "431857838950302", "2649144684462775" ]
[ "nonn" ]
22
0
4
[ "A000110", "A008277", "A048993", "A171367", "A320964", "A363071" ]
null
Alois P. Heinz, May 16 2023
2023-05-17T10:26:48
oeisdata/seq/A363/A363071.seq
b9e0102edb54cd08748c5182c62a496a
A363072
Add primes until a perfect power appears. When a perfect power appears, that term is the smallest root of the perfect power. Then return to adding primes, beginning with the next prime.
[ "2", "5", "10", "17", "28", "41", "58", "77", "10", "39", "70", "107", "148", "191", "238", "291", "350", "411", "478", "549", "622", "701", "28", "117", "214", "315", "418", "525", "634", "747", "874", "1005", "1142", "1281", "1430", "1581", "1738", "1901", "2068", "2241", "2420", "51", "242", "435", "632", "831", "1042", "1265", "1492", "1721", "1954", "2193" ]
[ "nonn", "easy" ]
9
1
1
[ "A001597", "A363072" ]
null
Damon Lay, May 16 2023
2023-06-23T17:04:35
oeisdata/seq/A363/A363072.seq
2ff558967ab9cc9f49a795e6f68831cb
A363073
Number of set partitions of [n] such that each element is contained in a block whose block size parity coincides with the parity of the element.
[ "1", "1", "0", "0", "1", "2", "0", "0", "20", "48", "0", "0", "1147", "3968", "0", "0", "173203", "709488", "0", "0", "53555964", "246505600", "0", "0", "28368601065", "148963383616", "0", "0", "24044155851601", "141410718244864", "0", "0", "30934515698084780", "198914201874983936", "0", "0", "57215369885233295955", "398742900995358584320" ]
[ "nonn" ]
37
0
6
[ "A000110", "A003724", "A005046", "A124419", "A274538", "A275679", "A363073" ]
null
Alois P. Heinz, May 17 2023
2023-11-18T04:02:20
oeisdata/seq/A363/A363073.seq
cb8f22b2b4b36dee03320de86e3cc4ef
A363074
Prime numbers that are the exact average of two consecutive odd semiprimes.
[ "23", "29", "37", "53", "61", "67", "73", "89", "103", "113", "131", "137", "157", "173", "211", "251", "277", "293", "307", "337", "379", "409", "449", "461", "487", "491", "499", "503", "523", "569", "617", "631", "661", "683", "701", "719", "727", "751", "769", "787", "919", "941", "953", "991", "1009", "1019", "1039", "1051", "1063", "1117", "1153", "1193", "1201", "1223", "1259", "1279", "1289", "1381", "1399" ]
[ "nonn" ]
41
1
1
[ "A000040", "A046315", "A363074", "A363187", "A363188" ]
null
Elmo R. Oliveira, May 20 2023
2023-07-05T12:19:53
oeisdata/seq/A363/A363074.seq
45071b1d0f80efec0b2cb20926704fd6
A363075
Number of partitions of n such that 3*(least part) + 1 = greatest part.
[ "0", "0", "0", "0", "1", "1", "2", "3", "6", "6", "10", "12", "18", "20", "27", "32", "42", "47", "59", "67", "85", "94", "113", "126", "152", "169", "198", "220", "257", "282", "326", "359", "413", "452", "512", "563", "639", "695", "781", "853", "958", "1041", "1161", "1261", "1402", "1524", "1685", "1827", "2021", "2186", "2407", "2604", "2861", "3088", "3385", "3657", "4002", "4316", "4704", "5069", "5531" ]
[ "nonn" ]
17
1
7
[ "A049820", "A237825", "A237828", "A363075", "A363076", "A363077" ]
null
Seiichi Manyama, May 17 2023
2025-06-20T02:35:37
oeisdata/seq/A363/A363075.seq
81879f8f6ff3d77fec52790fcd7cdf93
A363076
Number of partitions of n such that 4*(least part) + 1 = greatest part.
[ "0", "0", "0", "0", "0", "1", "1", "2", "3", "5", "8", "10", "14", "19", "25", "33", "41", "51", "65", "79", "97", "116", "140", "165", "198", "233", "272", "316", "369", "422", "493", "561", "643", "731", "835", "943", "1072", "1205", "1359", "1524", "1717", "1911", "2147", "2387", "2665", "2960", "3295", "3640", "4049", "4469", "4950", "5455", "6028", "6622", "7310", "8024", "8826", "9676", "10632", "11627", "12765" ]
[ "nonn" ]
12
1
8
[ "A049820", "A237826", "A237828", "A363075", "A363076", "A363077" ]
null
Seiichi Manyama, May 17 2023
2025-06-19T05:57:41
oeisdata/seq/A363/A363076.seq
3b167d30894d831201e94065ce4f7d4e
A363077
Number of partitions of n such that 5*(least part) + 1 = greatest part.
[ "0", "0", "0", "0", "0", "0", "1", "1", "2", "3", "5", "7", "12", "14", "21", "27", "37", "46", "63", "75", "97", "119", "149", "178", "222", "260", "317", "373", "447", "520", "620", "713", "839", "965", "1123", "1282", "1488", "1687", "1939", "2196", "2508", "2826", "3220", "3610", "4087", "4578", "5157", "5755", "6472", "7199", "8060", "8953", "9991", "11069", "12330", "13625", "15134", "16708", "18508" ]
[ "nonn" ]
13
1
9
[ "A049820", "A237827", "A237828", "A363075", "A363076", "A363077" ]
null
Seiichi Manyama, May 17 2023
2025-06-19T05:58:41
oeisdata/seq/A363/A363077.seq
ee9259b4f135121155105746ce2fa392
A363078
Decimal expansion of lim_{x->oo} (Sum_{k=2..x} 1 / (k*log(log(k)))) - li(log(x)).
[ "2", "7", "9", "7", "7", "6", "4", "7", "0", "3", "5", "2", "0", "8", "0", "4", "9", "2", "7", "6", "6", "0", "5", "0", "4", "5", "6", "5", "5", "3", "3", "5", "2", "8", "8", "4", "3", "3", "0", "8", "5", "0", "0", "8", "3", "2", "0", "2", "3", "2", "6", "9", "8", "9", "5", "7", "7", "8", "5", "6", "3", "1", "5", "0", "0", "5", "0", "6", "4", "3", "2", "8", "9", "3", "6", "2", "4", "5", "4", "5", "9", "4", "8", "3", "6", "8", "6", "8", "2", "5", "4", "8", "1", "8", "2", "9", "5", "4", "1", "9", "2", "5", "5", "0", "8" ]
[ "nonn", "cons" ]
18
1
1
[ "A077761", "A086242", "A137245", "A138312", "A221711", "A303493", "A319231", "A319232", "A354887", "A354917", "A354952", "A361089", "A361972", "A362533", "A363078", "A363368" ]
null
Artur Jasinski, Jun 11 2023
2023-08-26T15:34:55
oeisdata/seq/A363/A363078.seq
69a080afe2cc00549d99a06dd09b9893
A363079
The sum of the digits present in a(n) and a(n+1) divides exactly a(n). This is the lexicographically earliest infinite sequence of distinct positive terms having this property.
[ "10", "13", "18", "27", "99", "69", "17", "36", "12", "21", "22", "16", "45", "15", "54", "63", "39", "999", "19", "72", "30", "25", "189", "81", "198", "31", "1899", "499999999999999999999" ]
[ "base", "nonn" ]
30
1
1
[ "A363079", "A364120", "A364187", "A364188" ]
null
Eric Angelini, Jul 13 2023
2024-04-14T04:44:40
oeisdata/seq/A363/A363079.seq
fa074277aa31ced8d7bd5f30cc967705
A363080
Number of hexagonal lattice points within a hexagram centered at a lattice point and with outermost vertices at the six lattice points n steps outward from the central point.
[ "1", "7", "13", "25", "43", "61", "85", "115", "145", "181", "223", "265", "313", "367", "421", "481", "547", "613", "685", "763", "841", "925", "1015", "1105", "1201", "1303", "1405", "1513", "1627", "1741", "1861", "1987", "2113", "2245", "2383", "2521", "2665", "2815", "2965", "3121", "3283", "3445", "3613", "3787", "3961", "4141", "4327", "4513", "4705", "4903", "5101", "5305", "5515", "5725" ]
[ "nonn", "easy" ]
40
0
2
[ "A003154", "A004396", "A005448", "A007980", "A081272", "A363080" ]
null
Aaron David Fairbanks, May 17 2023
2025-02-06T15:35:39
oeisdata/seq/A363/A363080.seq
6c374860b9154953da8ad5cd1b45fac2
A363081
Decimal expansion of Product_{k>=1} (1 - exp(-11*Pi*k)).
[ "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "0", "1", "8", "5", "6", "8", "2", "4", "0", "6", "4", "6", "7", "6", "6", "7", "6", "8", "5", "3", "2", "4", "8", "9", "0", "1", "8", "6", "4", "9", "8", "5", "2", "3", "2", "4", "6", "5", "3", "1", "7", "4", "8", "5", "0", "1", "4", "4", "0", "7", "2", "2", "3", "2", "0", "8", "7", "3", "1", "8", "2", "0", "4", "7", "2", "7", "1", "7", "8", "5", "7", "6", "2", "3", "0", "8", "1", "6", "0", "2", "5", "5", "8", "6", "2", "2", "6", "0", "1", "2", "6" ]
[ "nonn", "cons" ]
9
0
1
[ "A259148", "A259149", "A259150", "A259151", "A292864", "A292888", "A292905", "A363018", "A363019", "A363020", "A363021", "A363081", "A363117", "A363118", "A363119", "A363120", "A363178", "A363179" ]
null
Vaclav Kotesovec, May 18 2023
2023-05-20T02:56:42
oeisdata/seq/A363/A363081.seq
331b2ca64e44abcc7afe3fcc62418766
A363082
Numbers k neither squarefree nor prime power such that q*r > k, where q = A053669(k) is the smallest prime that does not divide k and r = A007947(k) is the squarefree kernel.
[ "12", "18", "20", "24", "28", "44", "52", "60", "68", "76", "84", "90", "92", "116", "120", "124", "126", "132", "140", "148", "150", "156", "164", "168", "172", "180", "188", "198", "204", "212", "220", "228", "234", "236", "244", "260", "264", "268", "276", "284", "292", "306", "308", "312", "316", "332", "340", "342", "348", "356", "364", "372", "380", "388", "404", "408", "412", "414", "420" ]
[ "nonn" ]
48
1
1
[ "A007947", "A053669", "A126706", "A360765", "A360767", "A360768", "A363082" ]
null
Michael De Vlieger, Jul 29 2023
2023-08-02T13:55:14
oeisdata/seq/A363/A363082.seq
f8463c6b886130f3171adedfd8909343
A363083
a(0)=a(1)=1. For n>1, if the number of occurrences of a(n-1) is less than abs(a(n-1)), then a(n)=a(n-1)-a(n-2). Otherwise, a(n)=a(n-1)+a(n-2).
[ "1", "1", "2", "1", "3", "2", "5", "3", "-2", "-5", "-3", "2", "-1", "1", "0", "1", "1", "2", "3", "5", "2", "7", "5", "-2", "3", "1", "4", "3", "7", "4", "-3", "-7", "-4", "3", "-1", "2", "1", "3", "4", "1", "5", "4", "9", "5", "14", "9", "-5", "-14", "-9", "5", "-4", "-9", "-5", "4", "-1", "3", "2", "5", "7", "2", "9", "7", "-2", "5", "3", "8", "5", "13", "8", "-5", "-13", "-8", "5", "-3", "2", "-1", "1", "0" ]
[ "sign", "easy", "look" ]
38
0
3
[ "A329985", "A362746", "A362890", "A363083", "A363086" ]
null
Gavin Lupo, May 18 2023
2025-04-01T16:06:31
oeisdata/seq/A363/A363083.seq
b0ab82485458635349cf263e929ec191
A363084
Numbers k such that sqrt(A007947(k) - A007913(k)) is an integer m > 0.
[ "4", "16", "18", "25", "64", "72", "100", "162", "180", "256", "288", "289", "294", "400", "507", "625", "648", "676", "720", "722", "1024", "1152", "1176", "1210", "1369", "1458", "1600", "1620", "2178", "2205", "2500", "2548", "2592", "2646", "2704", "2880", "2888", "3150", "4096", "4225", "4500", "4563", "4608", "4704", "4840", "5202", "5832", "5887" ]
[ "nonn" ]
36
1
1
[ "A002496", "A003592", "A007913", "A007947", "A089653", "A363084", "A365517" ]
null
Michael De Vlieger, Sep 05 2023
2023-09-19T12:44:13
oeisdata/seq/A363/A363084.seq
bebde54453e8ce5ce278a92ce0444ec1
A363085
Sum of the refactorable unitary divisors of n.
[ "1", "3", "1", "1", "1", "3", "1", "9", "10", "3", "1", "13", "1", "3", "1", "1", "1", "30", "1", "1", "1", "3", "1", "33", "1", "3", "1", "1", "1", "3", "1", "1", "1", "3", "1", "46", "1", "3", "1", "49", "1", "3", "1", "1", "10", "3", "1", "1", "1", "3", "1", "1", "1", "3", "1", "65", "1", "3", "1", "73", "1", "3", "10", "1", "1", "3", "1", "1", "1", "3", "1", "90", "1", "3", "1", "1", "1", "3", "1", "81", "1", "3", "1", "97", "1", "3", "1", "97" ]
[ "nonn", "easy" ]
60
1
2
[ "A034444", "A336041", "A363085", "A363298" ]
null
Wesley Ivan Hurt, May 27 2023
2023-05-27T13:05:28
oeisdata/seq/A363/A363085.seq
760afcac70938951d76e238b1bc59b4d
A363086
a(0)=a(1)=1. For n>1, let c=count of all occurrences of a(n-1) in the list so far. If c < abs(a(n-1)), then a(n)=c-a(n-1). Otherwise, a(n)=c.
[ "1", "1", "2", "-1", "1", "3", "-2", "3", "-1", "2", "2", "3", "3", "4", "-3", "4", "-2", "2", "4", "-1", "3", "5", "-4", "5", "-3", "5", "-2", "3", "6", "-5", "6", "-4", "6", "-3", "3", "7", "-6", "7", "-5", "7", "-4", "7", "-3", "4", "4", "5", "-1", "4", "6", "-2", "4", "7", "-2", "5", "5", "6", "-1", "5", "7", "-1", "6", "6", "7", "7", "8", "-7", "8", "-6", "8", "-5", "8", "-4", "4", "8", "-3", "5", "8", "-2" ]
[ "sign", "easy", "look" ]
19
0
3
[ "A363083", "A363086" ]
null
Gavin Lupo, May 18 2023
2023-05-21T23:33:32
oeisdata/seq/A363/A363086.seq
827186001c1237e17ed60953992f836d
A363087
G.f. A(x) satisfies: A(x) = x - x^2 * exp(A(x) - A(x^2)/2 + A(x^3)/3 - A(x^4)/4 + ...).
[ "1", "-1", "-1", "1", "2", "-1", "-5", "-1", "11", "10", "-21", "-39", "30", "126", "4", "-354", "-261", "834", "1347", "-1483", "-5033", "823", "15663", "8765", "-41112", "-56364", "84888", "234546", "-91319", "-791833", "-293380", "2251507", "2561264", "-5177875", "-11835968", "7620048", "42944358", "7464956", "-130615874", "-119900209" ]
[ "sign" ]
10
1
5
[ "A007560", "A049075", "A345234", "A363062", "A363087" ]
null
Ilya Gutkovskiy, May 18 2023
2025-04-22T21:55:43
oeisdata/seq/A363/A363087.seq
688f24029e5abd4b48f95844c8607b97
A363088
Positive numbers k for which sin(k) >= cos(k).
[ "1", "2", "3", "8", "9", "10", "14", "15", "16", "20", "21", "22", "26", "27", "28", "29", "33", "34", "35", "39", "40", "41", "45", "46", "47", "52", "53", "54", "58", "59", "60", "64", "65", "66", "70", "71", "72", "73", "77", "78", "79", "83", "84", "85", "89", "90", "91", "96", "97", "98", "102", "103", "104", "108", "109", "110", "114", "115", "116", "117", "121", "122", "123", "127", "128", "129" ]
[ "nonn" ]
16
1
2
[ "A363088", "A363089" ]
null
Wolfe Padawer, May 18 2023
2023-07-04T23:55:34
oeisdata/seq/A363/A363088.seq
d3cf60ccaa3cb86d7b11b14fa8b324a6
A363089
Positive numbers k for which cos(k) > sin(k).
[ "4", "5", "6", "7", "11", "12", "13", "17", "18", "19", "23", "24", "25", "30", "31", "32", "36", "37", "38", "42", "43", "44", "48", "49", "50", "51", "55", "56", "57", "61", "62", "63", "67", "68", "69", "74", "75", "76", "80", "81", "82", "86", "87", "88", "92", "93", "94", "95", "99", "100", "101", "105", "106", "107", "111", "112", "113", "118", "119", "120", "124", "125", "126", "130", "131", "132" ]
[ "nonn" ]
16
1
1
[ "A363088", "A363089" ]
null
Wolfe Padawer, May 18 2023
2024-06-19T02:03:09
oeisdata/seq/A363/A363089.seq
e0f286f170c24a62c87bb63298f941de
A363090
Number of 3-dimensional directed animals of size n.
[ "1", "3", "12", "52", "237", "1113", "5339", "26011", "128247", "638346", "3201967", "16164384", "82044151", "418352107", "2141761669", "11003117220" ]
[ "nonn", "hard", "more" ]
19
1
2
[ "A005773", "A363090" ]
null
Joerg Arndt and Márk Péter Légrádi, May 19 2023
2024-11-21T19:25:11
oeisdata/seq/A363/A363090.seq
fde17737f499e67d83ecb106607fba84
A363091
Sum of the divisor complements of the refactorable unitary divisors of n.
[ "1", "3", "3", "4", "5", "9", "7", "9", "10", "15", "11", "13", "13", "21", "15", "16", "17", "30", "19", "20", "21", "33", "23", "28", "25", "39", "27", "28", "29", "45", "31", "32", "33", "51", "35", "41", "37", "57", "39", "46", "41", "63", "43", "44", "50", "69", "47", "48", "49", "75", "51", "52", "53", "81", "55", "64", "57", "87", "59", "66", "61", "93", "70", "64", "65", "99", "67", "68", "69", "105", "71" ]
[ "nonn", "easy" ]
30
1
2
[ "A034444", "A336041", "A363085", "A363091", "A363298" ]
null
Wesley Ivan Hurt, May 27 2023
2023-05-27T13:14:44
oeisdata/seq/A363/A363091.seq
4f9b6160c8892ede59924ddd064b6758
A363092
a(n) = 4*a(n-1) - 8*a(n-2) with a(0) = a(1) = 1.
[ "1", "1", "-4", "-24", "-64", "-64", "256", "1536", "4096", "4096", "-16384", "-98304", "-262144", "-262144", "1048576", "6291456", "16777216", "16777216", "-67108864", "-402653184", "-1073741824", "-1073741824", "4294967296", "25769803776", "68719476736", "68719476736", "-274877906944", "-1649267441664", "-4398046511104" ]
[ "sign", "easy" ]
11
0
3
[ "A000045", "A008586", "A088137", "A088138", "A363092" ]
null
Stefano Spezia, May 19 2023
2023-05-19T14:18:50
oeisdata/seq/A363/A363092.seq
fd9d96619f3cef2267cf8e3995da2c4f
A363093
Leading digit of 7^n.
[ "1", "7", "4", "3", "2", "1", "1", "8", "5", "4", "2", "1", "1", "9", "6", "4", "3", "2", "1", "1", "7", "5", "3", "2", "1", "1", "9", "6", "4", "3", "2", "1", "1", "7", "5", "3", "2", "1", "1", "9", "6", "4", "3", "2", "1", "1", "7", "5", "3", "2", "1", "1", "8", "6", "4", "3", "2", "1", "1", "7", "5", "3", "2", "1", "1", "8", "5", "4", "2", "2", "1", "1", "7", "4", "3", "2", "1", "1", "8", "5", "4", "2", "1", "1", "9", "6", "4", "3", "2", "1", "1", "8", "5", "3", "2", "1", "1", "9", "6", "4", "3" ]
[ "nonn", "base", "easy" ]
24
0
2
[ "A000030", "A000420", "A001903", "A008568", "A008952", "A060956", "A111395", "A362871", "A363093", "A363249", "A364185" ]
null
Seiichi Manyama, Jul 15 2023
2023-07-15T14:02:54
oeisdata/seq/A363/A363093.seq
a89123ee60310bc08e84b63d7920647a
A363094
Number of partitions of n whose least part is a multiple of 3.
[ "0", "0", "1", "0", "0", "2", "1", "1", "3", "2", "3", "6", "6", "7", "11", "11", "14", "21", "24", "29", "38", "44", "54", "69", "81", "98", "123", "144", "174", "213", "253", "300", "363", "427", "508", "608", "716", "846", "1004", "1176", "1384", "1631", "1908", "2230", "2616", "3046", "3553", "4143", "4813", "5586", "6492", "7509", "8693", "10057", "11608", "13383", "15435", "17753", "20418", "23463", "26923", "30864" ]
[ "nonn" ]
18
1
6
[ "A026805", "A363045", "A363094", "A363095", "A363096" ]
null
Seiichi Manyama, May 19 2023
2023-05-21T07:30:24
oeisdata/seq/A363/A363094.seq
c49e3dbee2f57e7b117ced26cb932e4c
A363095
Number of partitions of n whose least part is a multiple of 4.
[ "0", "0", "0", "1", "0", "0", "0", "2", "1", "1", "1", "3", "2", "3", "3", "7", "6", "8", "9", "13", "13", "17", "19", "28", "30", "38", "43", "56", "62", "76", "87", "110", "124", "151", "173", "211", "241", "289", "332", "399", "456", "539", "620", "733", "838", "983", "1127", "1322", "1513", "1761", "2016", "2343", "2677", "3096", "3536", "4083", "4655", "5355", "6101", "7005", "7969", "9124", "10370", "11856", "13453", "15340" ]
[ "nonn" ]
17
1
8
[ "A026805", "A363046", "A363094", "A363095", "A363096" ]
null
Seiichi Manyama, May 19 2023
2023-05-21T07:35:53
oeisdata/seq/A363/A363095.seq
ac07dcecc612f4ecf9edf8eed4b69d16
A363096
Number of partitions of n whose least part is a multiple of 5.
[ "0", "0", "0", "0", "1", "0", "0", "0", "0", "2", "1", "1", "1", "1", "3", "2", "3", "3", "4", "7", "7", "8", "10", "11", "15", "16", "19", "22", "27", "34", "39", "46", "54", "63", "76", "86", "101", "117", "136", "161", "186", "214", "249", "287", "335", "384", "445", "509", "588", "677", "776", "888", "1020", "1163", "1334", "1519", "1735", "1975", "2253", "2564", "2917", "3312", "3762", "4265", "4842", "5477", "6203", "7012", "7928" ]
[ "nonn" ]
21
1
10
[ "A026805", "A363047", "A363094", "A363095", "A363096" ]
null
Seiichi Manyama, May 19 2023
2023-05-21T10:20:35
oeisdata/seq/A363/A363096.seq
551a8f629a31a324f1a13d9b85196d68
A363097
a(0) = 1, a(n) = n + phi(a(n-1)), where phi is Euler totient function.
[ "1", "2", "3", "5", "8", "9", "12", "11", "18", "15", "18", "17", "28", "25", "34", "31", "46", "39", "42", "31", "50", "41", "62", "53", "76", "61", "86", "69", "72", "53", "82", "71", "102", "65", "82", "75", "76", "73", "110", "79", "118", "99", "102", "75", "84", "69", "90", "71", "118", "107", "156", "99", "112", "101", "154", "115", "144", "105", "106", "111", "132", "101", "162", "117", "136" ]
[ "nonn" ]
9
0
2
[ "A000010", "A363097" ]
null
Giorgos Kalogeropoulos, May 19 2023
2023-05-23T21:00:17
oeisdata/seq/A363/A363097.seq
60053d2459656853ed1c305242d061e9
A363098
Primitive terms of A363063.
[ "2", "12", "720", "864", "4320", "21600", "62208", "151200", "311040", "1555200", "7776000", "10886400", "54432000", "381024000", "4191264000", "160030080000", "251475840000", "1760330880000", "11522165760000", "19363639680000", "126743823360000", "251727315840000", "403275801600000", "829595934720000" ]
[ "nonn" ]
18
1
1
[ "A347284", "A363063", "A363098" ]
null
Pontus von Brömssen and Peter Munn, May 19 2023
2023-05-25T15:14:02
oeisdata/seq/A363/A363098.seq
ec068b38700f6403cb073df8c41546a9
A363099
Triangle T(n,k) in which the n-th row encodes the inverse of a 3n+1 X 3n+1 Jacobi matrix, with 1's on the lower, main, and upper diagonals in GF(2), where the encoding consists of the decimal representations for the binary rows (n >= 1, 1 <= k <= 3n+1).
[ "11", "3", "12", "13", "91", "27", "96", "107", "3", "108", "109", "731", "219", "768", "859", "27", "864", "875", "3", "876", "877", "5851", "1755", "6144", "6875", "219", "6912", "7003", "27", "7008", "7019", "3", "7020", "7021", "46811", "14043", "49152", "55003", "1755", "55296", "56027", "219", "56064", "56155", "27", "56160", "56171", "3", "56172", "56173", "374491", "112347", "393216", "440027", "14043", "442368" ]
[ "nonn", "base", "tabf" ]
51
1
1
[ "A010701", "A038184", "A083713", "A204623", "A245599", "A363099", "A363146" ]
null
Nei Y. Soma, May 20 2023
2023-05-25T15:12:41
oeisdata/seq/A363/A363099.seq
f74c41b672a3fa0a0ce2253f94c26e9e
A363100
Fractal sequence which is left unchanged by interleaving it with the natural numbers, in such a way that each term k of the sequence is followed by the next k not-yet-seen natural numbers.
[ "1", "2", "2", "3", "4", "2", "5", "6", "3", "7", "8", "9", "4", "10", "11", "12", "13", "2", "14", "15", "5", "16", "17", "18", "19", "20", "6", "21", "22", "23", "24", "25", "26", "3", "27", "28", "29", "7", "30", "31", "32", "33", "34", "35", "36", "8", "37", "38", "39", "40", "41", "42", "43", "44", "9", "45", "46", "47", "48", "49", "50", "51", "52", "53", "4", "54" ]
[ "nonn", "easy" ]
25
1
2
null
null
Allan C. Wechsler, May 20 2023
2023-11-04T14:00:17
oeisdata/seq/A363/A363100.seq
11e3bf972b5c55606621706f40665cd0