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1999-12-11 03:00:00
2026-01-19 02:46:49
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A391895
a(n) = Sum_{k=0..n} (k+1) * 2^k * binomial(2*k+1,2*n-2*k).
[ "1", "4", "24", "152", "812", "4192", "21312", "106048", "519568", "2516672", "12074112", "57467008", "271692992", "1277193216", "5974321152", "27825801216", "129109422336", "597042549760", "2752617871360", "12656462034944", "58052075088896", "265680602210304", "121345414...
[ "nonn" ]
14
0
2
[ "A390700", "A391832", "A391894", "A391895" ]
null
Seiichi Manyama, Dec 22 2025
2026-01-01T08:46:39
oeisdata/seq/A391/A391895.seq
9e8a475676ef1f412f1aa15ab5c30e09
A391896
Cubefull numbers with exactly 2 distinct prime factors.
[ "216", "432", "648", "864", "1000", "1296", "1728", "1944", "2000", "2592", "2744", "3375", "3456", "3888", "4000", "5000", "5184", "5488", "5832", "6912", "7776", "8000", "9261", "10000", "10125", "10368", "10648", "10976", "11664", "13824", "15552", "1...
[ "nonn", "easy" ]
10
1
1
[ "A001694", "A007774", "A013929", "A024619", "A036966", "A046099", "A126706", "A200511", "A286708", "A355462", "A372404", "A372695", "A376936", "A378767", "A391896" ]
null
Michael De Vlieger, Dec 23 2025
2025-12-24T04:11:06
oeisdata/seq/A391/A391896.seq
9b160f53d7c7639799a1e36888bed16c
A391897
Partial products of A063659.
[ "1", "2", "6", "18", "90", "540", "3780", "22680", "181440", "1814400", "19958400", "179625600", "2335132800", "32691859200", "490377888000", "5884534656000", "100037089152000", "1600593426432000", "30411275102208000", "456169126533120000", "9579551657195520000", "210750136...
[ "nonn", "easy" ]
7
1
2
[ "A001088", "A001615", "A059381", "A059382", "A059383", "A059384", "A063659", "A066780", "A066843", "A130779", "A175596", "A175836", "A239672", "A321613", "A322175", "A391897" ]
null
Amiram Eldar, Dec 23 2025
2025-12-23T04:22:15
oeisdata/seq/A391/A391897.seq
b654144f7a244e693bceacce9bfe2b70
A391898
The maximum exponent in the prime factorization of the exponentially noncomposite numbers (A390439).
[ "0", "1", "1", "2", "1", "1", "1", "3", "2", "1", "1", "2", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "3", "2", "1", "3", "2", "1", "1", "1", "5", "1", "1", "1", "2", "1", "1", "1", "3", "1", "1", "1", "2", "2", "1", "...
[ "nonn", "easy" ]
12
1
4
[ "A051903", "A375766", "A375768", "A390439", "A391898", "A391899" ]
null
Amiram Eldar, Dec 23 2025
2025-12-23T04:47:50
oeisdata/seq/A391/A391898.seq
d5eee8452b300c0250c1627afdb436b7
A391899
The maximum exponent in the prime factorization of the exponentially squarefree numbers (A209061).
[ "0", "1", "1", "2", "1", "1", "1", "3", "2", "1", "1", "2", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "3", "2", "1", "3", "2", "1", "1", "1", "5", "1", "1", "1", "2", "1", "1", "1", "3", "1", "1", "1", "2", "2", "1", "...
[ "nonn", "easy" ]
11
1
4
[ "A008683", "A051903", "A209061", "A262276", "A375766", "A375768", "A391898", "A391899" ]
null
Amiram Eldar, Dec 23 2025
2025-12-23T04:47:55
oeisdata/seq/A391/A391899.seq
2771c824e121fa5aed51aeacc8108e51
A391900
The total number of prime factors (counted with multiplicity) of the prime factorization exponents of n.
[ "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "2", "0", "1", "0", "1", "0", "0", "0", "1", "1", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "2", "0", "0", "0", "1", "0", "0", "0", "1", "1", "...
[ "nonn", "easy" ]
8
1
16
[ "A001222", "A005361", "A071325", "A362412", "A366073", "A376657", "A386262", "A389836", "A391900" ]
null
Amiram Eldar, Dec 23 2025
2025-12-23T04:20:49
oeisdata/seq/A391/A391900.seq
e77014a67f59db63a5b95ebde0b17307
A391901
The number of distinct factorials that are unitarily dividing n.
[ "1", "2", "1", "1", "1", "3", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "2", "1", "1", "1", "3", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "3", "1", "1", "1", "...
[ "nonn", "easy" ]
9
1
2
[ "A000010", "A000142", "A048855", "A055881", "A077610", "A123476", "A373318", "A373319", "A391901" ]
null
Amiram Eldar, Dec 23 2025
2025-12-23T04:20:25
oeisdata/seq/A391/A391901.seq
7398bfa5caf83f7dbdcea548e5fd40e4
A391902
a(n) = Sum_{k=0..n} binomial(3*k,3*(n-k)).
[ "1", "1", "2", "21", "86", "305", "1381", "6042", "24901", "105364", "450017", "1902321", "8044478", "34114553", "144535714", "612041073", "2592800365", "10984222558", "46527959417", "197093207976", "834913179137", "3536745086753", "14981831303770", "63464151953133", ...
[ "nonn" ]
19
0
3
[ "A003522", "A391902", "A391903", "A391904" ]
null
Seiichi Manyama, Dec 23 2025
2026-01-01T03:01:43
oeisdata/seq/A391/A391902.seq
b28943fc60928936c202b20ab9320f8e
A391903
a(n) = Sum_{k=0..floor(n/2)} binomial(3*k,3*(n-2*k)).
[ "1", "0", "1", "1", "1", "20", "2", "84", "85", "221", "925", "675", "5007", "5821", "19020", "49951", "72829", "296770", "428528", "1364693", "3001497", "5998390", "18112232", "31698490", "92287620", "193987770", "443261263", "1145617890", "2292692419", "61...
[ "nonn" ]
18
0
6
[ "A391902", "A391903", "A391904" ]
null
Seiichi Manyama, Dec 23 2025
2025-12-31T04:14:46
oeisdata/seq/A391/A391903.seq
13b1888eed47fbb01566f5e156e4e883
A391904
a(n) = Sum_{k=0..floor(n/3)} binomial(3*k,3*(n-3*k)).
[ "1", "0", "0", "1", "1", "0", "1", "20", "1", "1", "84", "84", "2", "220", "924", "221", "456", "5005", "5006", "1271", "18565", "48621", "19894", "55080", "293932", "295954", "188860", "1308835", "2707082", "1603514", "4821422", "17389944", "17977636"...
[ "nonn" ]
18
0
8
[ "A391902", "A391903", "A391904" ]
null
Seiichi Manyama, Dec 23 2025
2025-12-31T04:14:49
oeisdata/seq/A391/A391904.seq
40acc9afa7dd1db8a3fa79b21d94a032
A391905
Numbers which are the hypotenuse of a primitive Pythagorean quadruple whose legs are also members of a smaller primitive Pythagorean quadruple.
[ "49", "137", "161", "245", "257", "497", "637", "685", "805", "833", "1169", "1225", "1285", "1421", "1513", "1601", "1781", "1813", "1897", "1993", "2009", "2093", "2329", "2369", "2485", "2597", "2681", "2737", "2777", "2989", "3185", "3209", "3281",...
[ "nonn" ]
11
1
1
[ "A256418", "A391905" ]
null
Charles L. Hohn, Dec 23 2025
2025-12-30T19:52:12
oeisdata/seq/A391/A391905.seq
d0369cf181c731b23f8f707f17245495
A391906
Numerators of the convergents given by treating A390946 as continued fraction coefficients after the leading 0.
[ "1", "2", "5", "12", "17", "29", "75", "254", "583", "1420", "4843", "6263", "17369", "41001", "222374", "485749", "1679621", "2165370", "6010361", "14186092", "76940821", "91126913", "168067734", "259194647", "945651675", "5933104697", "12811861069", "571805489...
[ "nonn", "frac" ]
6
1
2
[ "A086702", "A390946", "A391906", "A391907" ]
null
Jwalin Bhatt, Dec 23 2025
2025-12-29T20:25:07
oeisdata/seq/A391/A391906.seq
e1a7c6331fab0327a872e11db9675726
A391907
Denominators of the convergents given by treating A390946 as continued fraction coefficients after the leading 0.
[ "1", "3", "7", "17", "24", "41", "106", "359", "824", "2007", "6845", "8852", "24549", "57950", "314299", "686548", "2373943", "3060491", "8494925", "20050341", "108746630", "128796971", "237543601", "366340572", "1336565317", "8385732474", "18108030265", "80817...
[ "nonn", "frac" ]
6
1
2
[ "A086702", "A390946", "A391906", "A391907" ]
null
Jwalin Bhatt, Dec 23 2025
2025-12-29T20:25:45
oeisdata/seq/A391/A391907.seq
5e617520a871976d994fe959495a60d2
A391908
Numbers k such that sigma(k) = psi(k) + phi(k) + omega(k)^5.
[ "1984", "2760", "24852", "36084", "49044", "57088", "245248", "377910", "1014784", "11507958", "16350500", "151632054", "170747262", "246570534", "463572774", "1011059264", "2035069974", "7980282656" ]
[ "nonn", "hard", "more" ]
15
1
1
[ "A000010", "A000203", "A001221", "A001615", "A390049", "A391312", "A391749", "A391763", "A391908" ]
null
S. I. Dimitrov, Dec 23 2025
2025-12-29T21:43:27
oeisdata/seq/A391/A391908.seq
d3dce224c1c97c9a3813912fce1e5a6a
A391909
Numbers k such that -1 <= A195017(k) <= 1.
[ "1", "2", "3", "5", "6", "7", "11", "12", "13", "14", "15", "17", "18", "19", "23", "26", "28", "29", "30", "31", "33", "35", "36", "37", "38", "41", "42", "43", "45", "47", "51", "52", "53", "58", "59", "61", "65", "66", "67", "69", "7...
[ "nonn", "easy", "new" ]
20
1
2
[ "A000040", "A073485", "A195017", "A206284", "A257991", "A257992", "A260442", "A260443", "A297845", "A325698", "A391746", "A391747", "A391909" ]
null
Antti Karttunen and Peter Munn, Dec 23 2025
2026-01-04T23:27:18
oeisdata/seq/A391/A391909.seq
a391fce9cd18a7893d61e6bd743aa500
A391910
Triangle read by rows: T(n,k) are the unique integer coefficients such that Sum_{k=0..n} T(n,k)*A125790(k,m)/2^(n*k) = (m+2)^n for all n >= 0, m >= 0.
[ "1", "1", "2", "1", "8", "16", "1", "26", "192", "384", "1", "80", "1696", "12288", "24576", "1", "242", "13440", "272640", "1966080", "3932160", "1", "728", "101296", "5222400", "104816640", "754974720", "1509949440", "1", "2186", "743232", "92663424", ...
[ "nonn", "tabl", "changed" ]
15
0
3
[ "A000120", "A125790", "A391910" ]
null
Mikhail Kurkov, Dec 23 2025
2026-01-17T16:33:17
oeisdata/seq/A391/A391910.seq
87af263cae983068c17391e40794e13b
A391911
Dimension of the space of twist-minimal newforms of weight 2 and level n.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "1", "0", "1", "0", "1", "1", "1", "0", "2", "1", "0", "2", "1", "0", "2", "1", "2", "1", "1", "1", "3", "1", "2", "2", "3", "1", "3", "1", "3", "1", "0", "...
[ "nonn" ]
16
1
23
[ "A001617", "A127788", "A391911" ]
null
Andrew R. Booker, Dec 23 2025
2025-12-29T23:10:26
oeisdata/seq/A391/A391911.seq
35bc2b3cdb0abaeabbb1b0d7642ffa0d
A391912
Number of irredundant sets in the n-triangular honeycomb queen graph.
[ "2", "4", "22", "76", "454", "3040", "23077", "202644", "2006095", "22326039" ]
[ "nonn", "more", "changed" ]
8
1
1
null
null
Eric W. Weisstein, Dec 23 2025
2026-01-18T18:00:09
oeisdata/seq/A391/A391912.seq
0241bfd997c312af015b47dfe8a73897
A391913
Number of irredundant sets in the Lingren-Sousslier graph on 6n+4 vertices.
[ "253", "5517", "124383", "2860318" ]
[ "nonn", "more" ]
4
1
1
null
null
Eric W. Weisstein, Dec 23 2025
2025-12-23T09:40:49
oeisdata/seq/A391/A391913.seq
250ddf1c8a08b6eec2d36b62af68b6c2
A391914
Number of irredundant sets in the n-Lucas cube graph.
[ "2", "5", "9", "49", "320", "10713", "2256637" ]
[ "nonn", "more" ]
4
1
1
null
null
Eric W. Weisstein, Dec 23 2025
2025-12-23T09:40:53
oeisdata/seq/A391/A391914.seq
b303308f23a849ae34cf04c5e27bdfd7
A391915
Number of irredundant sets in the n-Pell graph.
[ "3", "16", "544", "2220016" ]
[ "nonn", "more" ]
4
1
1
null
null
Eric W. Weisstein, Dec 23 2025
2025-12-23T09:41:02
oeisdata/seq/A391/A391915.seq
7d2933647322b747fe35d512854f9893
A391916
Number of irredundant sets in the n-trapezohedral graph.
[ "77", "192", "523", "1389", "3718", "10048", "27377", "75239", "208502", "582141", "1636305", "4626548", "13148533", "37534128", "107557937", "309242349", "891663491", "2577397759", "7466156079", "21668293968", "62988073938", "183360687221", "534427741078", "15593286198...
[ "nonn" ]
13
3
1
[ "A370089", "A391916" ]
null
Eric W. Weisstein, Dec 23 2025
2026-01-01T15:49:09
oeisdata/seq/A391/A391916.seq
3e2f500cd7e89d22a63626afd74c9f7c
A391917
Number of irredundant sets in the n-double cone graph.
[ "2", "10", "17", "122", "257", "577", "1850", "5626", "16901", "47525", "140626", "414737", "1223237", "3583450", "10523537", "30946970", "90973445", "267322501", "785456677", "2308418117", "6784157957", "19937157602", "58589654810", "172181842705", "506006018282", ...
[ "nonn", "easy", "changed" ]
24
1
1
[ "A290493", "A290494", "A391917", "A392237" ]
null
Eric W. Weisstein, Dec 23 2025
2026-01-08T13:48:52
oeisdata/seq/A391/A391917.seq
39572bf54ae3012963debc0ab79617bf
A391918
Number of irredundant sets in the n-triangular honeycomb acute knight graph.
[ "2", "8", "27", "144", "1331", "27000", "569344", "16777216", "1083206683", "85307250648", "9197641041408", "1896999488202671", "567844742926891708" ]
[ "nonn", "more" ]
4
1
1
null
null
Eric W. Weisstein, Dec 23 2025
2025-12-23T09:34:21
oeisdata/seq/A391/A391918.seq
a10234d26c00328c5e9f4ed87bd64419
A391920
Simple continued fraction expansion of (Pi - e*log(Pi))/(log(Pi) - 1).
[ "0", "4", "1", "5", "3", "3", "1", "1", "1", "2", "15", "1", "3", "1", "1", "21", "1", "10", "14", "1", "3", "2", "2", "2", "1", "16", "1", "1", "2", "1", "1", "2", "1", "2", "1", "37", "1", "2", "12", "3", "4", "2", "3", "2", "...
[ "nonn", "cofr", "easy" ]
10
0
2
[ "A001203", "A003417", "A259671", "A380965", "A391920" ]
null
Stefano Spezia, Dec 23 2025
2025-12-25T06:03:51
oeisdata/seq/A391/A391920.seq
729e0d3280fe5fb4e0bde5e7fb973a1a
A391921
Powerful numbers that are not cubefree and are divisible by exactly 2 distinct primes.
[ "72", "108", "144", "200", "216", "288", "324", "392", "400", "432", "500", "576", "648", "675", "784", "800", "864", "968", "972", "1000", "1125", "1152", "1296", "1323", "1352", "1372", "1568", "1600", "1728", "1936", "1944", "2000", "2025", "2304"...
[ "nonn", "easy", "new" ]
12
1
1
[ "A001694", "A007774", "A024619", "A046099", "A126706", "A286708", "A355462", "A372404", "A378767", "A391896", "A391921" ]
null
Michael De Vlieger, Dec 23 2025
2026-01-06T11:11:10
oeisdata/seq/A391/A391921.seq
647886c110ec5c65a917cf8e1bee550d
A391922
Numbers that are neither cubefree nor powerful and have exactly 2 distinct prime factors.
[ "24", "40", "48", "54", "56", "80", "88", "96", "104", "112", "135", "136", "152", "160", "162", "176", "184", "189", "192", "208", "224", "232", "248", "250", "272", "296", "297", "304", "320", "328", "344", "351", "352", "368", "375", "376", ...
[ "nonn", "new" ]
11
1
1
[ "A007774", "A013929", "A046099", "A054753", "A126706", "A200511", "A332785", "A345381", "A378767", "A391319", "A391922" ]
null
Michael De Vlieger, Dec 23 2025
2026-01-17T23:10:55
oeisdata/seq/A391/A391922.seq
cf644c5d741ec7a5b60ef270f7f11a52
A391923
Achilles numbers divisible by only 1 cube greater than 1.
[ "72", "108", "200", "288", "392", "500", "675", "800", "968", "972", "1125", "1152", "1323", "1352", "1372", "1568", "1800", "2312", "2700", "2888", "3087", "3200", "3267", "3528", "3872", "4232", "4500", "4563", "4608", "5292", "5324", "5408", "6075",...
[ "nonn", "easy" ]
17
1
1
[ "A001694", "A013929", "A024619", "A052486", "A082020", "A126706", "A286708", "A369632", "A390539", "A391923", "A391968" ]
null
Michael De Vlieger, Dec 25 2025
2026-01-04T10:44:44
oeisdata/seq/A391/A391923.seq
8c439df7d8906d03475682b3bc2a38e0
A391924
Numbers k such that (26^k - 5^k)/21 is prime.
[ "2", "79", "2621", "21841" ]
[ "nonn", "hard", "more" ]
5
1
1
[ "A062587", "A062589", "A127996", "A127997", "A128344", "A204940", "A217320", "A225807", "A229542", "A375161", "A375236", "A377031", "A391924" ]
null
Robert Price, Dec 23 2025
2025-12-23T14:01:54
oeisdata/seq/A391/A391924.seq
4e2bffafbefd042eb620826e1149f2b8
A391925
Square array read by descending antidiagonals: A(n, k) is the k-th natural number i that satisfies i*n = A048720(i,m) for some m, where A048720 is carryless base-2 multiplication.
[ "1", "2", "1", "3", "2", "1", "4", "3", "2", "1", "5", "4", "3", "2", "1", "6", "5", "4", "3", "2", "1", "7", "6", "5", "4", "3", "2", "1", "8", "7", "6", "5", "4", "3", "2", "1", "9", "8", "7", "6", "6", "4", "4", "2", "1", "...
[ "nonn", "base", "tabl" ]
27
1
2
[ "A000012", "A001477", "A048720", "A065621", "A115872", "A391585", "A391725", "A391740", "A391742", "A391744", "A391846", "A391848", "A391850", "A391852", "A391854", "A391856", "A391858", "A391860", "A391925", "A391926" ]
null
Antti Karttunen, Dec 23 2025
2025-12-23T15:27:45
oeisdata/seq/A391/A391925.seq
94f65750775d3667fdd4fa97a0dad4c5
A391926
Square array read by descending antidiagonals: find the k-th natural number i that satisfies i*n = A048720(i,m) for some m, then A(n, k) = m. Here A048720 is carryless base-2 multiplication.
[ "1", "1", "2", "1", "2", "3", "1", "2", "3", "4", "1", "2", "7", "4", "5", "1", "2", "3", "4", "5", "6", "1", "2", "3", "4", "5", "6", "7", "1", "2", "7", "4", "5", "14", "7", "8", "1", "2", "7", "4", "5", "6", "7", "8", "9", ...
[ "nonn", "base", "tabl" ]
21
1
3
[ "A000012", "A000027", "A000120", "A048720", "A280500", "A391726", "A391925", "A391926" ]
null
Antti Karttunen, Dec 23 2025
2025-12-29T15:08:48
oeisdata/seq/A391/A391926.seq
0f6ebce1c21980f20aeff20fc779fba3
A391927
Numbers k for which A373842(k) >= k, where A373842 is the arithmetic derivative of the primorial base log-function.
[ "5", "7", "11", "13", "17", "19", "21", "23", "28", "29", "31", "33", "34", "35", "37", "38", "39", "41", "43", "44", "46", "47", "49", "51", "52", "53", "55", "57", "58", "59", "61", "62", "65", "66", "67", "68", "69", "71", "73", "76", ...
[ "nonn", "new" ]
8
1
1
[ "A003415", "A276085", "A373842", "A373847", "A391927", "A391938" ]
null
Antti Karttunen, Jan 15 2026
2026-01-15T19:27:33
oeisdata/seq/A391/A391927.seq
343aab5461c6102ee87dbfb94bf390a8
A391928
Irregular table T(n, k) = (k*A002110(n-1)) mod prime(n), n >= 0, k = 0..prime(n)-1, read by rows, with row 0 = {0} by convention.
[ "0", "0", "1", "0", "2", "1", "0", "1", "2", "3", "4", "0", "2", "4", "6", "1", "3", "5", "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "0", "9", "5", "1", "10", "6", "2", "11", "7", "3", "12", "8", "4", "0", "8", "16"...
[ "nonn", "tabf", "look", "new" ]
19
0
5
[ "A002110", "A007504", "A060735", "A062347", "A079276", "A341805", "A391928", "A391929" ]
null
Antti Karttunen, Jan 04 2026
2026-01-06T10:05:17
oeisdata/seq/A391/A391928.seq
1f888ac4e99db90415f8c06e0fb86acd
A391929
Number of fixed points on row n of triangle A391930.
[ "1", "2", "2", "10", "10", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", ...
[ "nonn", "new" ]
43
0
2
[ "A002110", "A079276", "A341805", "A343405", "A360407", "A391928", "A391929", "A391930" ]
null
Antti Karttunen, Jan 03 2026
2026-01-05T23:24:57
oeisdata/seq/A391/A391929.seq
20900402ae48f5182659259ac23c30d0
A391930
Irregular triangle T(n, k) = Sum_{i=1..n} (k mod prime(i))*A002110(i-1), with n >= 0, and 0 <= k < A002110(n), read by rows. Here A002110(n) is the n-th primorial number.
[ "0", "0", "1", "0", "3", "4", "1", "2", "5", "0", "9", "16", "19", "26", "5", "6", "15", "22", "25", "2", "11", "12", "21", "28", "1", "8", "17", "18", "27", "4", "7", "14", "23", "24", "3", "10", "13", "20", "29", "0", "39", "76", ...
[ "nonn", "base", "tabf", "look", "changed" ]
40
0
5
[ "A002110", "A049345", "A143293", "A240673", "A276085", "A276086", "A360407", "A391929", "A391930", "A391931", "A391933", "A391934", "A391935" ]
null
Antti Karttunen, Dec 29 2025
2026-01-05T23:24:18
oeisdata/seq/A391/A391930.seq
6645a8e31229fd06423beb7e04d0e31c
A391931
Irregular triangle T(n, k) = A143293(n-1) + Sum_{i=1..n} (k mod prime(i))*A002110(i-1), with n >= 1, and 1 <= k <= A002110(n), read by rows, where A002110 are the primorials and A143293 are their partial sums.
[ "2", "1", "6", "7", "4", "5", "8", "3", "18", "25", "28", "35", "14", "15", "24", "31", "34", "11", "20", "21", "30", "37", "10", "17", "26", "27", "36", "13", "16", "23", "32", "33", "12", "19", "22", "29", "38", "9", "78", "115", "148...
[ "nonn", "tabf", "less" ]
17
1
1
[ "A002110", "A143293", "A240673", "A289234", "A391930", "A391931", "A391932" ]
null
Antti Karttunen, Dec 29 2025
2025-12-31T22:20:48
oeisdata/seq/A391/A391931.seq
87ed882e2db1bb75f6c446fc33566d96
A391932
Inverse permutation of A391931.
[ "2", "1", "8", "5", "6", "3", "4", "7", "38", "23", "18", "33", "28", "13", "14", "29", "24", "9", "34", "19", "20", "35", "30", "15", "10", "25", "26", "11", "36", "21", "16", "31", "32", "17", "12", "27", "22", "37", "248", "143", "10...
[ "nonn", "tabf" ]
9
1
1
[ "A002110", "A143293", "A360407", "A391931", "A391932" ]
null
Antti Karttunen, Dec 30 2025
2025-12-30T23:40:27
oeisdata/seq/A391/A391932.seq
579ed62f7c8b02d5d1018f8f3f36fe42
A391933
Irregular triangle T(n, k) = Product_{i=1..n} prime(i)^(k mod prime(i)), with n >= 0, and 0 <= k < A002110(n), read by rows.
[ "1", "1", "2", "1", "6", "9", "2", "3", "18", "1", "30", "225", "250", "1875", "18", "5", "150", "1125", "1250", "3", "90", "25", "750", "5625", "2", "15", "450", "125", "3750", "9", "10", "75", "2250", "625", "6", "45", "50", "375", "11250...
[ "nonn", "tabf" ]
25
0
3
[ "A000012", "A002110", "A276086", "A391930", "A391933" ]
null
Antti Karttunen, Dec 29 2025
2025-12-31T22:20:41
oeisdata/seq/A391/A391933.seq
175885c8842d015676204521b3c79ef0
A391934
Irregular triangle T(n, k) = Sum_{i=1..1+n} (A003415(k) mod prime(i))*A002110(i-1), with n >= 0, and 0 <= k < A002110(n), read by rows.
[ "0", "0", "0", "0", "0", "9", "9", "26", "9", "0", "0", "39", "39", "146", "39", "155", "39", "162", "186", "15", "39", "68", "39", "85", "52", "136", "39", "7", "39", "114", "92", "201", "39", "88", "92", "31", "193", "136", "39", "0", ...
[ "nonn", "tabf", "new" ]
13
0
6
[ "A002110", "A003415", "A143293", "A391930", "A391934", "A391935" ]
null
Antti Karttunen, Jan 05 2026
2026-01-05T16:55:22
oeisdata/seq/A391/A391934.seq
73a428edd2d6f3fcd887fcec01657824
A391935
Irregular triangle T(n, k) = Sum_{i=1..1+n} (A276086(k) mod prime(i))*A002110(i-1), with n >= 0, and 0 <= k < A002110(n), read by rows.
[ "1", "3", "4", "9", "16", "19", "6", "25", "18", "39", "76", "109", "186", "85", "138", "155", "92", "31", "60", "91", "180", "123", "34", "151", "90", "31", "60", "185", "152", "121", "30", "151", "90", "63", "124", "181", "150", "121", "3...
[ "nonn", "base", "tabf", "new" ]
11
0
2
[ "A002110", "A143293", "A276086", "A391930", "A391934", "A391935" ]
null
Antti Karttunen, Jan 05 2026
2026-01-05T16:55:28
oeisdata/seq/A391/A391935.seq
18884a8c1476bfd11678268d140c3262
A391936
a(n) = Sum_{i=1..A328404(n)} (A276086(n) mod prime(i))*A002110(i-1), where A276086 is the primorial base exp-function, and A328404(n) gives the length of A276086(n) in primorial base representation.
[ "1", "4", "1", "6", "25", "18", "5", "2", "1", "60", "91", "180", "3", "34", "151", "90", "1081", "2160", "185", "1832", "331", "450", "781", "1350", "1953", "1594", "1231", "16110", "21751", "13260", "15", "28", "7", "12", "19", "6", "5", "2...
[ "nonn", "base", "new" ]
13
0
2
[ "A000035", "A002110", "A143293", "A276086", "A328404", "A391930", "A391935", "A391936", "A391937" ]
null
Antti Karttunen, Jan 06 2026
2026-01-06T11:11:20
oeisdata/seq/A391/A391936.seq
3e80dd0b01947146ab5d063a84b10ee8
A391937
Numbers k such that A276086(k) = A391936(k).
[ "0", "3", "5", "6", "39", "41", "45", "69", "210", "2316", "30030", "510555", "510720", "9699690", "223092870" ]
[ "nonn", "base", "more", "new" ]
7
1
2
[ "A002110", "A048103", "A276086", "A343405", "A391936", "A391937" ]
null
Antti Karttunen, Jan 06 2026
2026-01-06T11:11:52
oeisdata/seq/A391/A391937.seq
dc59a06ae1ae45f1e1fec6dc6be7e494
A391938
Numbers k not divisible by p^p for any prime p, and for which A373842(k) >= k, where A373842 is the arithmetic derivative of the primorial base log-function.
[ "5", "7", "11", "13", "17", "19", "21", "23", "29", "31", "33", "34", "35", "37", "38", "39", "41", "43", "46", "47", "49", "51", "53", "55", "57", "58", "59", "61", "62", "65", "66", "67", "69", "71", "73", "77", "78", "79", "82", "83", ...
[ "nonn", "new" ]
13
1
1
[ "A003415", "A048103", "A276085", "A276086", "A351228", "A373842", "A373847", "A373848", "A391927", "A391938", "A391939" ]
null
Antti Karttunen, Jan 15 2026
2026-01-15T19:27:24
oeisdata/seq/A391/A391938.seq
e1149ff9c89bba9ccd1611c76eedac1e
A391939
Composite numbers k such that A003415(k) <= A276086(k), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.
[ "4", "6", "8", "9", "10", "12", "14", "15", "16", "18", "20", "21", "22", "24", "25", "26", "27", "28", "33", "34", "35", "38", "39", "40", "42", "44", "45", "46", "48", "49", "50", "51", "52", "54", "55", "56", "57", "58", "62", "63", ...
[ "nonn", "base", "new" ]
22
1
1
[ "A002808", "A003415", "A276085", "A276086", "A276150", "A351228", "A373848", "A391938", "A391939" ]
null
Antti Karttunen, Jan 15 2026
2026-01-15T19:27:28
oeisdata/seq/A391/A391939.seq
c4e68861b5a63d3a6beea44ecb0bca86
A391940
RSA numbers.
[ "1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139", "35794234179725868774991807832568455403003778024228226193532908190484670252364677411513516111204504060317568667", "227010481295437363334259960947493668895875336466084780038173258247009162675779735389791151574...
[ "nonn", "fini", "full" ]
15
1
1
[ "A046388", "A391940", "A391941", "A391942", "A391943", "A391944", "A391945" ]
null
Antti Karttunen, Dec 28 2025
2025-12-28T22:25:34
oeisdata/seq/A391/A391940.seq
2159b1f7d6c44897118560b9f2dd7c5d
A391941
The smaller prime factor of RSA numbers.
[ "37975227936943673922808872755445627854565536638199", "5846418214406154678836553182979162384198610505601062333", "327414555693498015751146303749141488063642403240171463406883", "3490529510847650949147849619903898133417764638493387843990820577", "39685999459597454290161126162883786067576449112810064832555157...
[ "nonn", "fini", "hard", "more" ]
8
1
1
[ "A020639", "A391940", "A391941", "A391942" ]
null
Antti Karttunen, Dec 28 2025
2025-12-28T22:25:26
oeisdata/seq/A391/A391941.seq
79c5974a2ea98a01b1f6871db7f3f9e5
A391942
The greater prime factor of RSA numbers.
[ "40094690950920881030683735292761468389214899724061", "6122421090493547576937037317561418841225758554253106999", "693342667110830181197325401899700641361965863127336680673013", "32769132993266709549961988190834461413177642967992942539798288533", "4553449864673597218840368689727440886435630126320506960099904...
[ "nonn", "fini", "hard", "more" ]
8
1
1
[ "A006530", "A391940", "A391941", "A391942" ]
null
Antti Karttunen, Dec 28 2025
2025-12-28T22:25:30
oeisdata/seq/A391/A391942.seq
cb413161959ed87ed830b988d83ebf58
A391943
Binary widths of RSA numbers.
[ "330", "364", "397", "426", "430", "463", "496", "512", "530", "563", "576", "596", "629", "640", "663", "696", "704", "729", "762", "768", "768", "795", "829", "862", "895", "896", "928", "962", "995", "1024", "1024", "1028", "1061", "1094", "1128...
[ "nonn", "base", "fini", "full" ]
7
1
1
[ "A070939", "A391940", "A391943", "A391944" ]
null
Antti Karttunen, Dec 28 2025
2025-12-28T22:12:55
oeisdata/seq/A391/A391943.seq
a38c944537f805da5f4869d34caed60f
A391944
Number of decimal digits of RSA numbers.
[ "100", "110", "120", "129", "130", "140", "150", "155", "160", "170", "174", "180", "190", "193", "200", "210", "212", "220", "230", "232", "232", "240", "250", "260", "270", "270", "280", "290", "300", "309", "309", "310", "320", "330", "340", "...
[ "nonn", "base", "fini", "full" ]
6
1
1
[ "A055642", "A391940", "A391943", "A391944", "A391945" ]
null
Antti Karttunen, Dec 28 2025
2025-12-28T22:12:59
oeisdata/seq/A391/A391944.seq
afd7a6992196b11c72b079cffd9261bb
A391945
Sum of decimal digits of RSA numbers.
[ "433", "469", "589", "620", "535", "652", "676", "721", "703", "790", "785", "811", "820", "806", "922", "901", "1009", "973", "1042", "1006", "1018", "1099", "1168", "1102", "1261", "1222", "1408", "1306", "1348", "1381", "1369", "1420", "1357", "14...
[ "nonn", "base", "fini", "full" ]
8
1
1
[ "A007953", "A391940", "A391944", "A391945" ]
null
Antti Karttunen, Dec 28 2025
2025-12-28T22:13:08
oeisdata/seq/A391/A391945.seq
0fef5aff5e9e333f2aa5116493c9b0cb
A391946
a(n) = A276085(n) mod 2310, where A276085 is the primorial base log-function.
[ "0", "1", "2", "2", "6", "3", "30", "3", "4", "7", "210", "4", "0", "31", "8", "4", "0", "5", "0", "8", "32", "211", "0", "5", "12", "1", "6", "32", "0", "9", "0", "5", "212", "1", "36", "6", "0", "1", "2", "9", "0", "33", "0", "2...
[ "nonn", "new" ]
12
1
3
[ "A276085", "A372576", "A391864", "A391946", "A392598" ]
null
Antti Karttunen, Jan 17 2026
2026-01-18T15:40:38
oeisdata/seq/A391/A391946.seq
168276185e8c72b08cd359724a47d9e6
A391947
Numbers k such that A003415(k) == A276085(k) (mod 2310) and A003415(k+1) == A276085(k+1) (mod 2310), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function. .
[ "1", "27717", "41577", "69297", "131667", "159387", "235617", "242547", "270267", "277197", "332637", "346497", "519747", "540537", "595977", "713787", "803877", "852387", "928617", "1025637", "1178097", "1205817", "1212747", "1247397", "1288977", "1316697", "1344...
[ "nonn", "new" ]
13
1
2
[ "A001221", "A001222", "A003415", "A276085", "A391864", "A391947" ]
null
Antti Karttunen, Jan 17 2026
2026-01-18T15:40:43
oeisdata/seq/A391/A391947.seq
eda8aa6bf17c6233199efb99a6350e9d
A391948
Primes p such that f(p) is prime and f(f(p)) = p, where f(k) = 10 * (10^(floor(log_10(k)) + 1) - 1)/9 - k.
[ "3", "5", "7", "13", "31", "37", "43", "67", "73", "79", "97", "113", "127", "139", "157", "163", "173", "181", "191", "199", "223", "227", "229", "233", "251", "257", "271", "281", "283", "313", "337", "349", "353", "359", "367", "383", "401",...
[ "nonn", "base", "changed" ]
66
1
1
[ "A068811", "A105279", "A391948" ]
null
Gavin A. Forrester, Dec 23 2025
2026-01-07T02:55:51
oeisdata/seq/A391/A391948.seq
91fe3ac92cf77016abd649fab249730c
A391949
Numbers k such that sigma(k) = psi(k) + phi(k) + omega(k)^6.
[ "48896", "77844", "384564", "410484", "505524", "622164", "682644", "718932", "747444", "777684", "783732", "1046430", "1220310", "2014110", "2558430", "3639510", "3642210", "3828510", "3881430", "4093110", "4130910", "13649130", "13806500", "18027344", "21758096", ...
[ "nonn", "changed" ]
11
1
1
[ "A000010", "A000203", "A001221", "A001615", "A390049", "A391312", "A391749", "A391763", "A391908", "A391949" ]
null
S. I. Dimitrov, Dec 23 2025
2026-01-05T03:58:34
oeisdata/seq/A391/A391949.seq
23b71123051ca0fda3d9bf76a5f1e827
A391950
Triangle T(n,k) of coefficients of polynomials arising from Gaussian-weighted Chebyshev integrals.
[ "2", "12", "0", "120", "8", "2", "1680", "160", "48", "0", "30240", "3360", "1064", "24", "2", "665280", "80640", "26208", "960", "108", "0", "17297280", "2217600", "731808", "33696", "4240", "48", "2", "518918400", "69189120", "23063040", "1216512", "...
[ "nonn", "tabl", "changed" ]
24
1
1
[ "A370706", "A391950" ]
null
Gabriele Celebre, Dec 23 2025
2026-01-08T22:04:27
oeisdata/seq/A391/A391950.seq
3b116824c6449651ab5ce108f069aae8
A391951
Decimal expansion of the volume of an Escher's solid with unit shorter edge length.
[ "6", "1", "5", "8", "4", "0", "2", "8", "7", "1", "3", "5", "6", "0", "0", "8", "1", "5", "4", "7", "6", "4", "2", "5", "3", "6", "5", "8", "6", "8", "7", "5", "4", "6", "1", "9", "3", "5", "7", "4", "4", "1", "8", "6", "8", "...
[ "nonn", "cons", "easy" ]
10
1
1
[ "A010482", "A020784", "A391653", "A391951", "A391952" ]
null
Paolo Xausa, Dec 23 2025
2025-12-25T09:37:45
oeisdata/seq/A391/A391951.seq
a371ee5f7d59ababad1fdb7b1b1bea6c
A391952
Decimal expansion of the surface area of an Escher's solid with unit shorter edge length.
[ "2", "2", "6", "2", "7", "4", "1", "6", "9", "9", "7", "9", "6", "9", "5", "2", "0", "7", "8", "0", "8", "2", "7", "0", "1", "9", "5", "8", "7", "3", "5", "5", "1", "6", "9", "2", "5", "7", "1", "1", "4", "7", "5", "0", "0", "...
[ "nonn", "cons", "easy" ]
7
2
1
[ "A002193", "A391654", "A391951", "A391952" ]
null
Paolo Xausa, Dec 24 2025
2025-12-25T09:37:35
oeisdata/seq/A391/A391952.seq
2d29dbe4bb20635b2855c56d5b7600f4
A391953
Decimal expansion of hypergeom([1/4, 1/2, 3/4], [2/3, 4/3], 1/27)/4.
[ "2", "5", "0", "9", "9", "2", "1", "5", "7", "4", "9", "0", "4", "9", "0", "8", "5", "1", "4", "1", "9", "8", "3", "4", "3", "8", "6", "1", "6", "3", "2", "6", "4", "9", "3", "4", "3", "6", "0", "5", "7", "7", "5", "3", "0", "...
[ "nonn", "cons" ]
10
0
1
[ "A019819", "A094214", "A130880", "A192918", "A382626", "A382627", "A391953" ]
null
Stefano Spezia, Dec 23 2025
2025-12-24T02:02:37
oeisdata/seq/A391/A391953.seq
d2388a61ee84408bebddf6cefdaa415f
A391955
Number of pairs of Dyck paths of length 2*n touching the axis at the same points.
[ "1", "1", "2", "7", "38", "274", "2350", "22531", "233292", "2555658", "29232554", "346013450", "4211121946", "52446977292", "666024794758", "8599676755883", "112647192598844", "1494224720878614", "20041069061550880", "271454315346852530", "3709291397981162290", "5108806605...
[ "nonn" ]
15
0
3
[ "A000108", "A001181", "A001246", "A391955" ]
null
Ludovic Schwob, Dec 23 2025
2025-12-27T18:04:25
oeisdata/seq/A391/A391955.seq
c5697246c610a04c7fbeacb33bb1fdfc
A391956
a(n) = 1/Product_{i = 1..n} w_i, where w_i is the i-th weight factor for Laguerre-Gauss quadrature of degree n.
[ "1", "1", "8", "486", "221184", "750000000", "18895680000000", "3531604429335150000", "4891710928142129430528000", "50181356668275133180188221767680", "3810801545415429046272000000000000000000", "2141591602439723039788666936461886800000000000000", "8904178923323813039189941618529553910755974...
[ "nonn" ]
10
0
3
[ "A387347", "A391956", "A391957" ]
null
A.H.M. Smeets, Dec 23 2025
2025-12-30T19:23:56
oeisdata/seq/A391/A391956.seq
06ec0d1ee09cbacf1eb418959697238e
A391957
Irregular triangle read by rows: exponents of the primes in the prime factorization of A391956(n) (primes in increasing order).
[ "3", "1", "5", "13", "3", "7", "1", "9", "12", "10", "7", "4", "6", "5", "13", "41", "2", "3", "11", "27", "32", "1", "9", "32", "24", "18", "7", "16", "16", "14", "5", "21", "46", "31", "10", "3", "19", "26", "21", "6", "1", "17", ...
[ "nonn", "tabf", "changed" ]
21
2
1
[ "A000040", "A000720", "A391956", "A391957" ]
null
A.H.M. Smeets, Dec 23 2025
2026-01-18T19:24:19
oeisdata/seq/A391/A391957.seq
a0809bcd19f8c9cc4810818a7597131f
A391958
First column of A391957.
[ "0", "0", "3", "1", "13", "7", "12", "4", "41", "27", "32", "16", "46", "26", "33", "11", "113", "83", "88", "56", "102", "66", "73", "35", "138", "94", "101", "55", "119", "69", "78", "26", "289", "227", "232", "168", "246", "178", "185", ...
[ "nonn", "new" ]
50
0
3
[ "A001511", "A391956", "A391957", "A391958", "A392083" ]
null
A.H.M. Smeets, Dec 23 2025
2026-01-13T13:40:39
oeisdata/seq/A391/A391958.seq
da5c7193024b5464caa5105d6678a5dd
A391959
Second column of A391957.
[ "0", "0", "0", "5", "3", "1", "10", "6", "2", "32", "24", "16", "31", "21", "11", "30", "18", "6", "64", "48", "32", "57", "39", "21", "50", "30", "10", "149", "123", "97", "130", "102", "74", "111", "81", "51", "163", "129", "95", "138",...
[ "nonn", "new" ]
32
0
4
[ "A051064", "A391956", "A391957", "A391959", "A392084" ]
null
A.H.M. Smeets, Dec 28 2025
2026-01-13T13:40:27
oeisdata/seq/A391/A391959.seq
6c34f5978743ee088253e2348651dd26
A391960
a(n) = Sum_{k=0..floor(n/3)} (k+1) * 2^k * 3^(n-3*k) * binomial(k,2*(n-3*k)).
[ "1", "0", "0", "4", "0", "0", "12", "36", "0", "32", "288", "0", "80", "1440", "720", "192", "5760", "8640", "448", "20160", "60480", "13120", "64512", "322560", "195840", "193536", "1451520", "1746944", "739584", "5806080", "11623424", "5253120", "212...
[ "nonn", "easy" ]
18
0
4
[ "A390775", "A390781", "A391960", "A391961" ]
null
Seiichi Manyama, Dec 23 2025
2025-12-29T18:54:19
oeisdata/seq/A391/A391960.seq
1c936d4ee8a0214ebea349deb3054384
A391961
a(n) = Sum_{k=0..floor(n/3)} 2^k * 3^(n-3*k) * binomial(k+6,6) * binomial(k,2*(n-3*k)).
[ "1", "0", "0", "14", "0", "0", "112", "336", "0", "672", "6048", "0", "3360", "60480", "30240", "14784", "443520", "665280", "59136", "2661120", "7983360", "1816320", "13837824", "69189120", "42282240", "64576512", "484323840", "583751168", "339026688", "290...
[ "nonn" ]
14
0
4
[ "A390775", "A391723", "A391960", "A391961" ]
null
Seiichi Manyama, Dec 23 2025
2025-12-24T09:56:16
oeisdata/seq/A391/A391961.seq
e5979ece577e59d276a41111dc019f10
A391962
a(n) = Sum_{k=0..n} (k+1) * binomial(k,2*(n-k)).
[ "1", "2", "3", "7", "17", "36", "72", "143", "282", "549", "1057", "2019", "3832", "7232", "13581", "25394", "47303", "87819", "162549", "300060", "552552", "1015259", "1861674", "3407433", "6226053", "11358407", "20691504", "37642816", "68395609", "12412720...
[ "nonn" ]
19
0
2
[ "A005251", "A381421", "A391962", "A391963" ]
null
Seiichi Manyama, Dec 23 2025
2025-12-29T12:30:30
oeisdata/seq/A391/A391962.seq
ddb4d9926982b279f2d8b1ea62f8477a
A391963
a(n) = Sum_{k=0..n} binomial(k+2,2) * binomial(k,2*(n-k)).
[ "1", "3", "6", "16", "45", "111", "253", "561", "1221", "2603", "5448", "11238", "22906", "46206", "92361", "183151", "360636", "705672", "1373067", "2658129", "5122275", "9829497", "18790449", "35794569", "67966000", "128667132", "242906916", "457397132", "85...
[ "nonn", "easy" ]
19
0
2
[ "A005251", "A382230", "A391962", "A391963" ]
null
Seiichi Manyama, Dec 23 2025
2025-12-29T18:54:36
oeisdata/seq/A391/A391963.seq
da9679154c403dc1b3c24e384ae271f8
A391964
a(n) = Sum_{k=0..n} (k+1) * 2^k * binomial(k,2*(n-k)).
[ "1", "4", "12", "44", "176", "672", "2448", "8704", "30528", "105920", "364032", "1241088", "4202752", "14150656", "47410176", "158157824", "525602816", "1740840960", "5748461568", "18930761728", "62190206976", "203850235904", "666838499328", "2177331363840", "7097215...
[ "nonn" ]
16
0
2
[ "A390700", "A391964" ]
null
Seiichi Manyama, Dec 23 2025
2025-12-30T11:42:00
oeisdata/seq/A391/A391964.seq
f526299a1e464cdbda15ca9ae0d06317
A391965
a(n) = Sum_{k=0..n} 2^k * binomial(k+2,2) * binomial(k,2*(n-k)).
[ "1", "6", "24", "104", "480", "2112", "8752", "34848", "135168", "513792", "1920000", "7071744", "25728256", "92622336", "330405888", "1169217536", "4108296192", "14344470528", "49802211328", "172027060224", "591476293632", "2025119416320", "6907067105280", "23474916556...
[ "nonn" ]
17
0
2
[ "A391875", "A391965" ]
null
Seiichi Manyama, Dec 23 2025
2025-12-30T11:42:04
oeisdata/seq/A391/A391965.seq
0bd89bd3d4bca4e545fee2381c2de733
A391966
Smallest integer k greater than 1 such that every solution of y^m = y (for all integers m > 1) in the commutative ring of n-adic integers is also a solution of y^k = y.
[ "3", "3", "3", "5", "3", "7", "3", "3", "5", "11", "3", "13", "7", "5", "3", "17", "3", "19", "5", "7", "11", "23", "3", "5", "13", "3", "7", "29", "5", "31", "3", "11", "17", "13", "3", "37", "19", "13", "5", "41", "7", "43", "11",...
[ "nonn", "easy", "new" ]
26
2
1
[ "A007947", "A076566", "A373387", "A390598", "A390915", "A391966" ]
null
Marco Ripà, Dec 24 2025
2026-01-13T08:04:40
oeisdata/seq/A391/A391966.seq
c6bd2c20dc198796f46065c9ee97078e
A391967
Numbers k such that sigma(k) + phi(k) = psi(k) + k.
[ "1", "672", "3120", "7800", "11904", "23712", "55552", "195072", "302784", "492864", "910336", "1607808", "1671072", "1750656", "6688560", "13210368", "15242496", "16125952", "16721400", "17033984", "17274624", "26854656", "56755968", "633404992", "805208064", "8745...
[ "nonn" ]
19
1
2
[ "A000010", "A000203", "A001615", "A391967" ]
null
Kaloian Ivanov, Dec 24 2025
2025-12-31T16:20:29
oeisdata/seq/A391/A391967.seq
f69be171183b9537fac60d3e429de5b8
A391968
Numbers divisible by at least 2 cubes greater than 1.
[ "216", "432", "648", "864", "1000", "1080", "1296", "1512", "1728", "1944", "2000", "2160", "2376", "2592", "2744", "2808", "3000", "3024", "3240", "3375", "3456", "3672", "3888", "4000", "4104", "4320", "4536", "4752", "4968", "5000", "5184", "5400", ...
[ "nonn", "easy", "new" ]
13
1
1
[ "A002117", "A004709", "A013929", "A024619", "A046099", "A052486", "A126706", "A286229", "A286708", "A332785", "A372404", "A372695", "A375145", "A376936", "A378767", "A383394", "A388293", "A388304", "A388549", "A391319", "A391506", "A391968" ]
null
Michael De Vlieger, Dec 24 2025
2026-01-06T11:11:07
oeisdata/seq/A391/A391968.seq
a95aae525b493a65c549271183ebf517
A391969
Number of quotients of the lattice of alternating sign matrices of size n isomorphic to the lattice of Dyck paths of length 2*n.
[ "1", "1", "2", "6", "28", "202", "2252", "38756", "1028964", "42127054", "2658809724", "258630414936", "38767099255644", "8953246419943732", "3185558965388036052", "1745990974619361729172", "1474075441986980210547940", "1916876508718560362050901170", "3839234705282352916635502966...
[ "nonn", "changed" ]
16
1
3
[ "A000108", "A005130", "A390493", "A391969", "A391973" ]
null
Ludovic Schwob, Dec 24 2025
2026-01-11T21:38:29
oeisdata/seq/A391/A391969.seq
aba8da24eee89610a7cb78edda849500
A391970
Numbers m such that the product m*(m+1) has a set of prime divisors, from greatest down to 2, that is missing exactly two prime divisors.
[ "7", "10", "11", "32", "39", "84", "119", "143", "153", "168", "209", "220", "242", "272", "285", "324", "351", "374", "441", "455", "494", "624", "675", "728", "1224", "1539", "1700", "2057", "2184", "2499", "2600", "3059", "3135", "4913", "5082",...
[ "nonn" ]
13
1
1
[ "A391602", "A391885", "A391970" ]
null
Ken Clements, Dec 24 2025
2026-01-01T15:50:30
oeisdata/seq/A391/A391970.seq
6bb8a0675ba15fe94f47db4dcc1c33a5
A391971
Triangle read by rows: T(n,k) = number of heapable permutations of length n with exactly k 321 patterns.
[ "1", "1", "1", "2", "5", "14", "3", "42", "18", "11", "132", "82", "84", "27", "22", "11", "1", "429", "339", "456", "256", "243", "143", "124", "61", "43", "28", "4" ]
[ "nonn", "tabf", "more", "new" ]
20
1
4
[ "A336282", "A391697", "A391776", "A391777", "A391971" ]
null
Manolopoulos Panagiotis, Dec 24 2025
2026-01-18T12:56:14
oeisdata/seq/A391/A391971.seq
b08280cf137b06ac9f187a8771f915ff
A391973
Number of self-dual Catalan triangles of size 2*n+1.
[ "1", "2", "10", "120", "3434", "233876", "37866212" ]
[ "nonn", "more" ]
9
0
2
[ "A390493", "A391969", "A391973" ]
null
Ludovic Schwob, Dec 25 2025
2025-12-30T11:39:21
oeisdata/seq/A391/A391973.seq
96394157fddff47a4d8f33326b1914eb
A391975
Number of irredundant sets in the n-triangular honeycomb bishop graph.
[ "2", "5", "19", "94", "559", "3958", "32957" ]
[ "nonn", "more" ]
4
1
1
null
null
Eric W. Weisstein, Dec 25 2025
2025-12-25T09:37:05
oeisdata/seq/A391/A391975.seq
21930c68efd87fef39f608f1aaae507d
A391976
Number of irredundant sets in the n-triangular honeycomb obtuse knight graph.
[ "2", "8", "64", "250", "2256", "25591" ]
[ "nonn", "more" ]
4
1
1
null
null
Eric W. Weisstein, Dec 25 2025
2025-12-25T09:37:01
oeisdata/seq/A391/A391976.seq
04cf2edc88cf9bd91e8da9c5f6e405e0
A391978
a(n) = 2*n*binomial(n, 4).
[ "0", "0", "0", "8", "50", "180", "490", "1120", "2268", "4200", "7260", "11880", "18590", "28028", "40950", "58240", "80920", "110160", "147288", "193800", "251370", "321860", "407330", "510048", "632500", "777400", "947700", "1146600", "1377558", "1644300",...
[ "nonn", "easy", "new" ]
15
1
4
[ "A027764", "A391978" ]
null
Eric W. Weisstein, Dec 25 2025
2026-01-08T03:04:19
oeisdata/seq/A391/A391978.seq
f796916532e67bcd9de1998c381d89d3
A391979
Number of closed "knight + wazir" tours on an 8 X n board.
[ "0", "4", "1484", "290247", "21767466", "10808297353", "2375931620966", "460170137868876", "86120998813237562", "20912440756793175381", "4269789533989878923996", "903074393101632744082459", "186843783417066650757163898", "40434310805094436324334667019", "8440630895242498970832101406644" ...
[ "nonn" ]
11
1
2
[ "A193055", "A391979" ]
null
Don Knuth, Dec 25 2025
2025-12-25T19:45:39
oeisdata/seq/A391/A391979.seq
abdceca28de0d63a693715b243ef122e
A391980
Achilles numbers divisible by at least 2 cubes greater than 1.
[ "432", "648", "864", "1944", "2000", "2592", "3456", "3888", "4000", "5000", "5400", "5488", "6912", "9000", "10125", "10368", "10584", "10800", "10976", "13500", "15552", "16000", "16200", "16875", "17496", "18000", "19208", "20000", "21168", "21296", "21...
[ "nonn", "easy", "new" ]
11
1
1
[ "A001694", "A013929", "A024619", "A052486", "A072102", "A082020", "A082695", "A126706", "A286708", "A369632", "A388293", "A391968", "A391980" ]
null
Michael De Vlieger, Dec 26 2025
2026-01-06T11:11:14
oeisdata/seq/A391/A391980.seq
a295985872c432554f571f4bdf817318
A391981
Irregular triangle read by rows where row n lists the trimmed zero-based partial alternating sums of the prime indices of n.
[ "1", "2", "1", "0", "3", "1", "1", "4", "1", "0", "1", "2", "0", "1", "2", "5", "1", "0", "2", "6", "1", "3", "2", "1", "1", "0", "1", "0", "7", "1", "1", "1", "8", "1", "0", "3", "2", "2", "1", "4", "9", "1", "0", "1", "1", "...
[ "nonn", "tabf", "new" ]
14
2
2
[ "A000070", "A000097", "A000302", "A001222", "A028260", "A055396", "A056239", "A061395", "A103919", "A112798", "A124754", "A209281", "A239830", "A247180", "A283050", "A316524", "A344606", "A344610", "A344611", "A344612", "A344616", "A345958", "A346633", "A346697", "A34...
null
Gus Wiseman, Dec 26 2025
2026-01-11T17:53:45
oeisdata/seq/A391/A391981.seq
0d49d6da70da8a0fbd9e5f3041a375ec
A391982
Irregular triangle read by rows where row n lists the trimmed zero-based partial alternating sums of the reversed prime indices of n.
[ "1", "2", "1", "0", "3", "2", "-1", "4", "1", "0", "1", "2", "0", "3", "-2", "5", "2", "-1", "2", "6", "4", "-3", "3", "-1", "1", "0", "1", "0", "7", "2", "0", "1", "8", "3", "-2", "3", "4", "-2", "5", "-4", "9", "2", "-1", "2", ...
[ "sign", "tabf", "new" ]
7
2
2
[ "A000070", "A000097", "A001222", "A028260", "A055396", "A056239", "A061395", "A070003", "A102750", "A103919", "A112798", "A209281", "A239830", "A247180", "A316524", "A344606", "A344610", "A344611", "A344612", "A344616", "A345958", "A346633", "A346697", "A346699", "A34...
null
Gus Wiseman, Jan 11 2026
2026-01-12T08:42:31
oeisdata/seq/A391/A391982.seq
b8349ece7c42ed0c186fdc8a00ae0053
A391983
Irregular triangle read by rows where row n lists the trimmed zero-based partial alternating sums of the n-th composition in standard order.
[ "1", "2", "1", "0", "3", "2", "-1", "1", "1", "1", "0", "1", "4", "3", "-2", "2", "0", "2", "-1", "2", "1", "2", "1", "1", "0", "1", "0", "2", "1", "0", "1", "0", "5", "4", "-3", "3", "-1", "3", "-2", "3", "2", "1", "2", "0", "1...
[ "sign", "tabf", "new" ]
9
1
2
[ "A000120", "A003242", "A005674", "A011782", "A025047", "A065120", "A066099", "A070939", "A116406", "A124754", "A124767", "A209281", "A316524", "A342527", "A344616", "A344618", "A344619", "A346633", "A346697", "A346699", "A357213", "A390432", "A390567", "A390568", "A39...
null
Gus Wiseman, Jan 10 2026
2026-01-11T17:54:03
oeisdata/seq/A391/A391983.seq
716c254584c182b2da36e7a0f57701a0
A391984
Irregular triangle read by rows where row n lists the trimmed zero-based partial alternating sums of the reversed n-th composition in standard order.
[ "1", "2", "1", "0", "3", "1", "1", "2", "-1", "1", "0", "1", "4", "1", "2", "2", "0", "1", "0", "2", "3", "-2", "1", "1", "0", "2", "-1", "2", "1", "0", "1", "0", "5", "1", "3", "2", "1", "1", "0", "3", "3", "-1", "1", "1", "1",...
[ "sign", "tabf", "new" ]
5
1
2
[ "A000120", "A001511", "A003242", "A005674", "A011782", "A025047", "A065120", "A066099", "A070939", "A116406", "A124754", "A124767", "A209281", "A316524", "A342527", "A344616", "A344618", "A344619", "A346633", "A346697", "A346699", "A357213", "A390432", "A390567", "A39...
null
Gus Wiseman, Jan 11 2026
2026-01-12T08:42:27
oeisdata/seq/A391/A391984.seq
4044bf2d523b197a0c892f66d5b84d74
A391985
a(n) = Sum_{k=0..floor(n/4)} (k+1) * 2^k * 3^(n-3*k) * binomial(n-2*k,k) * binomial(n-3*k,k).
[ "1", "3", "9", "27", "105", "459", "2025", "8667", "36369", "151875", "636417", "2679075", "11308761", "47779227", "201873465", "852827211", "3602606625", "15218565363", "64287833841", "271557920115", "1146975813225", "4843839405771", "20453167820457", "86349979376667",...
[ "nonn" ]
14
0
2
[ "A098473", "A098482", "A390830", "A391985", "A391986" ]
null
Seiichi Manyama, Dec 26 2025
2025-12-31T14:26:08
oeisdata/seq/A391/A391985.seq
cb22518790362e992c862959871363e3
A391986
a(n) = Sum_{k=0..floor(n/4)} 2^k * 3^(n-3*k) * binomial(k+2,2) * binomial(n-2*k,k) * binomial(n-3*k,k).
[ "1", "3", "9", "27", "117", "567", "2673", "11907", "51597", "222831", "968841", "4236219", "18551781", "81154791", "354374433", "1545091443", "6729252957", "29281369023", "127304349273", "552981937419", "2399866971381", "10405820054007", "45080675201457", "195138858704...
[ "nonn", "changed" ]
19
0
2
[ "A098473", "A098482", "A390830", "A391985", "A391986" ]
null
Seiichi Manyama, Dec 26 2025
2026-01-05T15:15:17
oeisdata/seq/A391/A391986.seq
31ee5d6b3517347ea50a6df961c4797d
A391987
Decimal expansion of (7*sqrt(5)-5)/22.
[ "4", "8", "4", "2", "0", "3", "4", "4", "7", "3", "8", "6", "2", "9", "6", "7", "2", "1", "5", "8", "4", "7", "3", "7", "0", "7", "6", "4", "1", "4", "4", "9", "6", "9", "8", "4", "0", "0", "3", "8", "3", "3", "1", "1", "4", "...
[ "nonn", "cons" ]
5
0
1
[ "A000032", "A001566", "A001622", "A189961", "A391987" ]
null
Amiram Eldar, Dec 26 2025
2025-12-26T16:02:29
oeisdata/seq/A391/A391987.seq
62880086a227da31a2051b99781c7d22
A391988
The number of exponential divisors of the exponentially squarefree numbers.
[ "1", "1", "1", "2", "1", "1", "1", "2", "2", "1", "1", "2", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "2", "2", "1", "2", "2", "1", "1", "1", "2", "1", "1", "1", "4", "1", "1", "1", "2", "1", "1", "1", "2", "2", "1", "...
[ "nonn", "easy" ]
9
1
4
[ "A049419", "A074823", "A209061", "A262276", "A278908", "A388973", "A391988", "A391989" ]
null
Amiram Eldar, Dec 26 2025
2025-12-29T04:02:44
oeisdata/seq/A391/A391988.seq
3622853df3a47bae8de23ca2bc24d239
A391989
The difference between the number of exponential divisors and the number of exponential unitary divisors for numbers that are not exponentially squarefree.
[ "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "2", "1", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "2", "1", "2", "2", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "...
[ "nonn", "easy" ]
9
1
6
[ "A000005", "A001221", "A049419", "A130897", "A174961", "A262276", "A278908", "A322791", "A361255", "A391988", "A391989" ]
null
Amiram Eldar, Dec 26 2025
2025-12-29T04:02:25
oeisdata/seq/A391/A391989.seq
5366befee08ab30ac734ad4de470ce61
A391990
a(n) = Sum_{k=0..floor(n/2)} (k+1) * binomial(n,k) * binomial(n-k,k).
[ "1", "1", "5", "13", "43", "131", "411", "1275", "3963", "12283", "38023", "117503", "362605", "1117429", "3439229", "10572957", "32468787", "99610515", "305313711", "935015271", "2861204529", "8749050009", "26734768305", "81642292977", "249169635477", "760033085301...
[ "nonn", "changed" ]
18
0
3
[ "A002426", "A098473", "A391990" ]
null
Seiichi Manyama, Dec 26 2025
2026-01-05T15:15:31
oeisdata/seq/A391/A391990.seq
25ddc5424cbfa84342d20fda5bb249bb
A391991
Triangle read by rows: T(n,k) = number of digits in decimal representation of binomial(n,k), 0<=k<=n.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "1", "1", "2", "2", "2", "1", "1", "1", "1", "2", "2", "2", "2", "1", "1", "1", "1", "2", "2", "2", "2", "2", "1", "1", "...
[ "nonn", "tabl", "easy", "base" ]
12
0
18
[ "A007318", "A055642", "A101598", "A391991", "A391992" ]
null
Seiichi Manyama, Dec 26 2025
2025-12-26T08:32:02
oeisdata/seq/A391/A391991.seq
88f8b35f73fce2a54895b9f3530f6fdb
A391992
Number of digits in the decimal expansion of binomial(2*n,n).
[ "1", "1", "1", "2", "2", "3", "3", "4", "5", "5", "6", "6", "7", "8", "8", "9", "9", "10", "10", "11", "12", "12", "13", "13", "14", "15", "15", "16", "16", "17", "18", "18", "19", "19", "20", "21", "21", "22", "22", "23", "24", "24",...
[ "nonn", "easy", "base", "changed" ]
17
0
4
[ "A000984", "A055642", "A391991", "A391992" ]
null
Seiichi Manyama, Dec 26 2025
2026-01-05T15:15:02
oeisdata/seq/A391/A391992.seq
f8f27e35abdb3650d99a3bce537eae6b
A391993
Expansion of (2*x*(x - 7))/(x - 1)^3.
[ "0", "14", "40", "78", "128", "190", "264", "350", "448", "558", "680", "814", "960", "1118", "1288", "1470", "1664", "1870", "2088", "2318", "2560", "2814", "3080", "3358", "3648", "3950", "4264", "4590", "4928", "5278", "5640", "6014", "6400", "679...
[ "nonn", "easy", "new" ]
15
0
2
[ "A391993", "A392248" ]
null
Peter Luschny, Jan 09 2026
2026-01-10T19:16:04
oeisdata/seq/A391/A391993.seq
e3b0174bafe45e2195690b2ae58dd906
A391994
Expansion of (x^2*(3*x - 1))/((x - 1)^4*(x + 1)).
[ "0", "0", "-1", "0", "2", "8", "17", "32", "52", "80", "115", "160", "214", "280", "357", "448", "552", "672", "807", "960", "1130", "1320", "1529", "1760", "2012", "2288", "2587", "2912", "3262", "3640", "4045", "4480", "4944", "5440", "5967", "...
[ "sign", "easy", "new" ]
12
0
5
[ "A002620", "A391994", "A392248" ]
null
Peter Luschny, Jan 09 2026
2026-01-10T19:16:14
oeisdata/seq/A391/A391994.seq
4f3b35766d6ff1464160e3cd30c93fcf
A391995
a(n) = (4*n^3 - 18*n^2 - 4*n + 9*(1 - (-1)^n)) / 48.
[ "0", "0", "-1", "-1", "-1", "1", "4", "10", "18", "30", "45", "65", "89", "119", "154", "196", "244", "300", "363", "435", "515", "605", "704", "814", "934", "1066", "1209", "1365", "1533", "1715", "1910", "2120", "2344", "2584", "2839", "3111", ...
[ "sign", "easy", "new" ]
13
0
7
[ "A212964", "A391995", "A392248" ]
null
Peter Luschny, Jan 09 2026
2026-01-10T07:21:20
oeisdata/seq/A391/A391995.seq
53d97a996acfce05472451311cd70281
A391996
Table read by rows: T(n, k) = floor((k/2)^2)*n^2.
[ "0", "0", "0", "0", "0", "4", "0", "0", "9", "18", "0", "0", "16", "32", "64", "0", "0", "25", "50", "100", "150", "0", "0", "36", "72", "144", "216", "324", "0", "0", "49", "98", "196", "294", "441", "588", "0", "0", "64", "128", "256"...
[ "nonn", "tabl", "new" ]
15
0
6
[ "A212766", "A391996", "A391997" ]
null
Peter Luschny, Jan 10 2026
2026-01-11T05:09:16
oeisdata/seq/A391/A391996.seq
ec151977717f46750027d6f77400e7da
A391997
a(n) = Sum_{k=0..n} floor((k/2)^2)*n^2. Row sums of A391996.
[ "0", "0", "4", "27", "112", "325", "792", "1666", "3200", "5670", "9500", "15125", "23184", "34307", "49392", "69300", "95232", "128316", "170100", "222015", "286000", "363825", "457864", "570262", "703872", "861250", "1045772", "1260441", "1509200", "179553...
[ "nonn", "new" ]
10
0
3
[ "A391997" ]
null
Peter Luschny, Jan 10 2026
2026-01-10T08:51:18
oeisdata/seq/A391/A391997.seq
bc587496eaa567394b9ba1f27498cd59
A391998
Composite numbers k such that k + 1 is not a power of an odd prime and 2*k + 1 is not a prime power.
[ "25", "27", "32", "34", "38", "45", "49", "55", "57", "64", "76", "77", "85", "87", "91", "92", "93", "94", "104", "110", "115", "117", "118", "122", "123", "129", "132", "133", "142", "143", "145", "147", "152", "154", "159", "160", "161", "...
[ "nonn", "changed" ]
16
1
1
[ "A093880", "A391998", "A392001" ]
null
Peter Luschny, Jan 01 2026
2026-01-07T21:17:30
oeisdata/seq/A391/A391998.seq
0b400a99d114c99f0e10263a226ada82
A391999
Number of undirected closed knight's tours on a 9 X (2n) board.
[ "0", "0", "3374967940", "7112881119092574" ]
[ "nonn", "more" ]
9
1
3
[ "A000004", "A001230", "A169764", "A175855", "A175881", "A193054", "A193055", "A391999", "A392000", "X2" ]
null
Peter Luschny, Dec 27 2025
2025-12-27T13:06:04
oeisdata/seq/A391/A391999.seq
b793ca4399fc443e491b09f8aff66613