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1999-12-11 03:00:00
2025-04-28 00:58:08
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A357601
For n a power of 2, a(n) = n; otherwise, if 2^m is the greatest power of 2 not exceeding n and if k = n-2^m, then a(n) is the smallest number having d(a(k))+1 divisors which has not occurred earlier (d is the divisor counting function A000005).
[ "1", "2", "3", "4", "5", "9", "25", "8", "7", "49", "121", "6", "169", "10", "14", "16", "11", "289", "361", "15", "529", "21", "22", "81", "841", "26", "27", "625", "33", "2401", "14641", "32", "13", "961", "1369", "34", "1681", "35", "38", "28561", "1849", "39", "46", "83521", "51", "130321", "279841", "12", "2209", "55", "57", "707281", "58", "923521", "1874161", "18" ]
[ "nonn" ]
16
1
2
[ "A000005", "A005940", "A063787", "A357601" ]
null
David James Sycamore, Oct 05 2022
2022-10-06T10:31:56
oeisdata/seq/A357/A357601.seq
682726ee5d73e0a7d95e500294d83c9a
A357602
a(n) is the number of n-gons in A000940 that are asymmetric.
[ "0", "0", "0", "1", "15", "121", "1026", "8696", "81515", "827282", "9200052" ]
[ "nonn", "more" ]
42
3
5
[ "A000940", "A342533", "A357602" ]
null
Ian Mooney, Oct 05 2022
2022-11-01T07:15:01
oeisdata/seq/A357/A357602.seq
47814a7f658575db05190c2e73758c33
A357603
a(n) is the number of different pairs of shortest paths in an n X n lattice going between opposite corners in opposite directions and not meeting at their middle point.
[ "0", "2", "18", "236", "3090", "42252", "589932", "8383608", "120720402", "1756863020", "25789460268", "381298472568", "5671808350572", "84807208655288", "1273785187835640", "19207311526394736", "290631247129611282", "4411188317020786668", "67137528193253129484", "1024357917198436543800" ]
[ "nonn", "easy" ]
59
0
2
[ "A002894", "A005260", "A357603" ]
null
Janaka Rodrigo, Oct 05 2022
2022-11-19T12:45:33
oeisdata/seq/A357/A357603.seq
73b9f34b62e43430b152831bf5801d8a
A357604
Number of prime powers in the sequence of the floor of n/k for k <= n, A010766.
[ "0", "1", "1", "2", "2", "2", "3", "4", "4", "4", "5", "4", "5", "6", "6", "8", "8", "7", "8", "7", "8", "10", "11", "9", "10", "11", "12", "12", "13", "11", "12", "14", "14", "15", "16", "14", "15", "16", "17", "16", "17", "16", "17", "18", "18", "20", "21", "19", "21", "21", "21", "22", "23", "22", "23", "23", "24", "26", "27", "22", "23", "24", "25", "28", "28", "28", "29", "29", "30", "30", "31", "27" ]
[ "nonn" ]
39
1
4
[ "A000961", "A010766", "A025487", "A135972", "A357604" ]
null
Randell Heyman, Oct 06 2022
2022-11-19T21:58:24
oeisdata/seq/A357/A357604.seq
080800fa996f74b9d65fddae79b073d3
A357605
Numbers k such that A162296(k) > 2*k.
[ "36", "48", "72", "80", "96", "108", "120", "144", "160", "162", "168", "180", "192", "200", "216", "224", "240", "252", "264", "270", "280", "288", "300", "312", "320", "324", "336", "352", "360", "378", "384", "392", "396", "400", "408", "416", "432", "448", "450", "456", "468", "480", "486", "500", "504", "528", "540", "552", "560", "576", "588", "594", "600", "612" ]
[ "nonn" ]
12
1
1
[ "A005101", "A013929", "A034683", "A064597", "A129575", "A129656", "A162296", "A292982", "A348274", "A348604", "A357605" ]
null
Amiram Eldar, Oct 06 2022
2022-10-26T07:59:31
oeisdata/seq/A357/A357605.seq
5f943b6bb433c80612e6e88088645438
A357606
Primitive terms of A357605: numbers in A357605 with no proper divisor in A357605.
[ "36", "48", "80", "120", "162", "168", "200", "224", "264", "270", "280", "300", "312", "352", "378", "392", "408", "416", "450", "456", "500", "552", "588", "594", "630", "696", "700", "702", "744", "750", "882", "888", "918", "968", "980", "984", "1026", "1032", "1050", "1088", "1100", "1128", "1216", "1232", "1242", "1272", "1300", "1372", "1416", "1452" ]
[ "nonn" ]
10
1
1
[ "A005101", "A013929", "A091191", "A162296", "A302574", "A357605", "A357606" ]
null
Amiram Eldar, Oct 06 2022
2022-10-09T04:22:49
oeisdata/seq/A357/A357606.seq
1d94ecff8252af2b74f9b596bbdcc101
A357607
Odd numbers k such that A162296(k) > 2*k.
[ "4725", "6615", "7875", "8505", "11025", "14175", "15435", "17325", "19845", "20475", "22275", "23625", "24255", "25515", "26775", "28665", "29925", "31185", "33075", "36225", "36855", "37125", "37485", "38115", "39375", "40425", "41895", "42525", "46305", "47775", "48195", "50715", "51975", "53235", "53865", "55125", "57915", "59535" ]
[ "nonn" ]
11
1
1
[ "A005231", "A013929", "A094889", "A127666", "A129485", "A162296", "A293186", "A321147", "A348275", "A348605", "A357605", "A357607" ]
null
Amiram Eldar, Oct 06 2022
2022-10-09T04:22:46
oeisdata/seq/A357/A357607.seq
637796533e77e8db255cfd59614d28b9
A357608
Numbers k such that k and k+1 are both in A357605.
[ "76544", "104895", "126224", "165375", "170624", "174824", "201824", "245024", "257984", "271215", "273104", "316575", "338624", "387855", "447615", "469664", "477224", "540224", "618975", "633555", "641024", "659295", "705375", "752895", "770175", "842624", "843975", "862784", "870975", "893024", "913275", "957824", "1047375" ]
[ "nonn" ]
9
1
1
[ "A013929", "A096399", "A162296", "A283418", "A318167", "A327635", "A327942", "A331412", "A333951", "A357605", "A357608" ]
null
Amiram Eldar, Oct 06 2022
2022-10-09T04:22:42
oeisdata/seq/A357/A357608.seq
8d0ba605148f66086403dfd27d67c7a5
A357609
Numbers k such that k, k+1, and k+2 are all in A357605.
[ "10667829248", "14322877568", "25929352448", "26967189248", "31315096448", "32186016224", "35337613310", "36312573374", "41326711424", "53162460350", "69405075584", "71840196350", "72806666750", "73217757248", "83103523424", "106184935934", "109302242048", "111640866974", "115294917374", "116768901248" ]
[ "nonn" ]
9
1
1
[ "A013929", "A096536", "A162296", "A357605", "A357608", "A357609" ]
null
Amiram Eldar, Oct 06 2022
2022-10-09T04:22:39
oeisdata/seq/A357/A357609.seq
de239f86185d9c6e77f88603a2c16a8a
A357610
Start with x = 3 and repeat the map x -> floor(n/x) + (n mod x) until an x occurs that has already appeared, then that is a(n).
[ "1", "2", "3", "2", "3", "3", "3", "4", "3", "4", "3", "3", "5", "6", "3", "6", "5", "3", "7", "5", "3", "8", "7", "3", "9", "6", "3", "10", "9", "3", "11", "8", "3", "12", "5", "3", "13", "10", "3", "14", "9", "3", "15", "11", "3", "16", "11", "3", "17", "5", "3", "18", "5", "3", "19", "12", "3", "20", "11", "3", "21", "14", "3", "22", "5", "3", "23", "8", "3", "24", "15", "3", "25", "14", "3", "26", "17", "3", "27", "5", "3", "28", "11", "3", "29", "18", "3", "30", "9" ]
[ "nonn", "look" ]
15
1
2
[ "A357554", "A357610" ]
null
J. M. Bergot and Robert Israel, Oct 06 2022
2022-10-17T09:45:45
oeisdata/seq/A357/A357610.seq
a1215bb487a31ff9f727126d3c7d6e65
A357611
A refinement of the Mahonian numbers (canonical ordering).
[ "1", "1", "1", "1", "2", "2", "1", "1", "3", "5", "3", "3", "5", "3", "1", "1", "4", "9", "9", "6", "4", "16", "11", "11", "16", "4", "6", "9", "9", "4", "1", "1", "5", "14", "19", "10", "14", "35", "5", "40", "26", "19", "61", "10", "40", "26", "35", "35", "26", "40", "10", "61", "19", "26", "40", "5", "35", "14", "10", "19", "14", "5", "1" ]
[ "nonn", "tabf" ]
78
1
5
[ "A008302", "A060351", "A335845", "A356802", "A357611", "A360308" ]
null
Denis K. Sunko, Oct 06 2022
2024-12-28T10:18:36
oeisdata/seq/A357/A357611.seq
998e14fd9f9cb00b177813e6953059ad
A357612
Numbers k such that 1 + 2^k*k^3 is prime.
[ "1", "5", "41", "202", "281", "394", "1157", "1211", "1816", "9845", "19780", "50800", "98621", "101945" ]
[ "nonn", "more", "hard" ]
89
1
2
[ "A000040", "A005849", "A058780", "A357612" ]
null
Juri-Stepan Gerasimov, Nov 17 2022
2023-05-17T08:42:25
oeisdata/seq/A357/A357612.seq
13278edbebc1a029f198c3bbf5036b26
A357613
Triangle read by rows T(n, k) = binomial(2*n, k) * binomial(3*n - k, 2*n).
[ "1", "3", "2", "15", "20", "6", "84", "168", "105", "20", "495", "1320", "1260", "504", "70", "3003", "10010", "12870", "7920", "2310", "252", "18564", "74256", "120120", "100100", "45045", "10296", "924", "116280", "542640", "1058148", "1113840", "680680", "240240", "45045", "3432" ]
[ "nonn", "tabl", "easy" ]
26
0
2
[ "A000984", "A005809", "A026000", "A033282", "A110608", "A144485", "A243660", "A357613" ]
null
F. Chapoton, Oct 06 2022
2023-10-11T11:04:19
oeisdata/seq/A357/A357613.seq
2b2c059f4e0dfcc03d087f6d694fa622
A357614
Lexicographically earliest infinite sequence of distinct positive integers such that a(n+1) is the least k != j, for which gcd(k, j) > 1, where j = a(n) + prime(n).
[ "1", "6", "3", "2", "12", "46", "118", "5", "4", "9", "8", "13", "10", "15", "14", "122", "7", "11", "16", "166", "18", "21", "20", "206", "25", "22", "24", "254", "19", "26", "278", "27", "28", "30", "39", "32", "33", "34", "394", "17", "35", "36", "31", "37", "23", "38", "42", "44", "45", "40", "538", "48", "41", "47", "50", "614", "1754", "49", "52", "56", "674", "29", "54", "57", "58" ]
[ "nonn" ]
8
1
2
[ "A347113", "A349472", "A357595", "A357614" ]
null
David James Sycamore, Oct 06 2022
2022-10-21T15:12:25
oeisdata/seq/A357/A357614.seq
5cec5b52554e56c6aa6398fddb60f757
A357615
Expansion of e.g.f. cosh(sqrt(3) * (exp(x) - 1)).
[ "1", "0", "3", "9", "30", "135", "705", "3906", "22953", "145053", "985800", "7136613", "54544485", "437961888", "3685605735", "32441696325", "297977767662", "2848636972971", "28278241848309", "290931124989546", "3097051613077269", "34064462020306473", "386600759467746528", "4521440483724439521" ]
[ "nonn" ]
25
0
3
[ "A065143", "A264036", "A357572", "A357615", "A357681" ]
null
Seiichi Manyama, Oct 06 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357615.seq
9e785e66c1cb881d1178d4cbba43f492
A357616
Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the number of 1's in the ternary expansion of n equals the number of 2's in the ternary expansion of a(n) and vice versa.
[ "0", "2", "1", "6", "8", "5", "3", "7", "4", "18", "20", "11", "24", "26", "17", "15", "23", "14", "9", "19", "10", "21", "25", "16", "12", "22", "13", "54", "56", "29", "60", "62", "35", "33", "47", "32", "72", "74", "51", "78", "80", "53", "59", "71", "44", "45", "61", "34", "65", "77", "50", "38", "52", "41", "27", "55", "28", "57", "69", "42", "30", "46", "31", "63", "73", "48", "75", "79" ]
[ "nonn", "base" ]
11
0
2
[ "A004488", "A005823", "A005836", "A039001", "A062756", "A081603", "A352760", "A357616" ]
null
Rémy Sigrist, Oct 06 2022
2022-10-10T03:19:41
oeisdata/seq/A357/A357616.seq
74918d241737cb18f5be83351e7ab9f5
A357617
Expansion of e.g.f. sinh( (exp(4*x) - 1)/4 ).
[ "0", "1", "4", "17", "88", "657", "6844", "83393", "1072880", "14242785", "197046964", "2895895345", "45930435016", "789930042865", "14628150636012", "287915593953889", "5950831121362656", "128180962018224833", "2868724306984850020", "66704877850797014353", "1613138176448134032440" ]
[ "nonn" ]
26
0
3
[ "A009599", "A024429", "A356572", "A357617", "A357650" ]
null
Seiichi Manyama, Oct 07 2022
2022-10-07T15:47:03
oeisdata/seq/A357/A357617.seq
17c390d57f6fe8d7e2b96d09e0bafae7
A357618
a(n) = sum of lengths of partitions of more than one consecutive positive integer adding up to n.
[ "0", "0", "0", "2", "0", "2", "3", "2", "0", "5", "4", "2", "3", "2", "4", "10", "0", "2", "7", "2", "5", "11", "4", "2", "3", "7", "4", "11", "7", "2", "12", "2", "0", "11", "4", "14", "11", "2", "4", "11", "5", "2", "14", "2", "8", "25", "4", "2", "3", "9", "9", "11", "8", "2", "16", "17", "7", "11", "4", "2", "16", "2", "4", "27", "0", "17", "18", "2", "8", "11", "16" ]
[ "nonn", "easy" ]
56
0
4
[ "A069283", "A138591", "A204217", "A357618" ]
null
Daniel Vik, Oct 06 2022
2022-11-20T02:03:02
oeisdata/seq/A357/A357618.seq
b9d1375415a946e2512eab729903052b
A357619
Length of longest induced path (or chordless path) in the n-Fibonacci cube graph.
[ "0", "1", "2", "3", "6", "9", "13", "20", "30" ]
[ "nonn", "hard", "more" ]
17
0
3
[ "A099155", "A357619", "A357620" ]
null
Pontus von Brömssen, Oct 06 2022
2022-12-23T16:23:18
oeisdata/seq/A357/A357619.seq
db88023e95c123c13c065f4c1aa2d4bb
A357620
Length of longest induced cycle (or chordless cycle) in the n-Fibonacci cube graph.
[ "0", "0", "0", "4", "4", "10", "14", "18", "30", "46" ]
[ "nonn", "hard", "more" ]
12
0
4
[ "A000937", "A297668", "A357619", "A357620" ]
null
Pontus von Brömssen, Oct 06 2022
2022-12-03T05:55:18
oeisdata/seq/A357/A357620.seq
aa4c5f45e8fa867c93aef2a52bce391e
A357621
Half-alternating sum of the n-th composition in standard order.
[ "0", "1", "2", "2", "3", "3", "3", "1", "4", "4", "4", "2", "4", "2", "0", "0", "5", "5", "5", "3", "5", "3", "1", "1", "5", "3", "1", "1", "-1", "-1", "-1", "1", "6", "6", "6", "4", "6", "4", "2", "2", "6", "4", "2", "2", "0", "0", "0", "2", "6", "4", "2", "2", "0", "0", "0", "2", "-2", "-2", "-2", "0", "-2", "0", "2", "2", "7", "7", "7", "5", "7", "5", "3", "3", "7", "5", "3", "3", "1", "1", "1", "3", "7", "5", "3", "3", "1" ]
[ "sign" ]
11
0
3
[ "A001511", "A053251", "A357136", "A357182", "A357183", "A357184", "A357185", "A357621", "A357622", "A357623", "A357624", "A357625", "A357626", "A357627", "A357628", "A357629", "A357630", "A357631", "A357633", "A357634", "A357635", "A357637", "A357638", "A357639", "A357640", "A357641", "A357642" ]
null
Gus Wiseman, Oct 07 2022
2022-10-08T08:34:20
oeisdata/seq/A357/A357621.seq
8faf95c314daf292f17554c37122c19f
A357622
Half-alternating sum of the reversed n-th composition in standard order.
[ "0", "1", "2", "2", "3", "3", "3", "1", "4", "4", "4", "0", "4", "2", "2", "0", "5", "5", "5", "-1", "5", "1", "1", "-1", "5", "3", "3", "-1", "3", "1", "1", "1", "6", "6", "6", "-2", "6", "0", "0", "-2", "6", "2", "2", "-2", "2", "0", "0", "2", "6", "4", "4", "-2", "4", "0", "0", "0", "4", "2", "2", "0", "2", "2", "2", "2", "7", "7", "7", "-3", "7", "-1", "-1", "-3", "7", "1", "1", "-3", "1", "-1", "-1", "3", "7", "3" ]
[ "sign" ]
9
0
3
[ "A001511", "A053251", "A124754", "A344618", "A357136", "A357182", "A357183", "A357184", "A357185", "A357621", "A357622", "A357623", "A357624", "A357625", "A357626", "A357627", "A357628", "A357629", "A357631", "A357633", "A357635", "A357637", "A357638", "A357639", "A357641", "A357642" ]
null
Gus Wiseman, Oct 08 2022
2022-10-08T09:42:10
oeisdata/seq/A357/A357622.seq
ca8e5c76b98c1f77b3058e7d4be67acb
A357623
Skew-alternating sum of the n-th composition in standard order.
[ "0", "1", "2", "0", "3", "1", "-1", "-1", "4", "2", "0", "0", "-2", "-2", "-2", "0", "5", "3", "1", "1", "-1", "-1", "-1", "1", "-3", "-3", "-3", "-1", "-3", "-1", "1", "1", "6", "4", "2", "2", "0", "0", "0", "2", "-2", "-2", "-2", "0", "-2", "0", "2", "2", "-4", "-4", "-4", "-2", "-4", "-2", "0", "0", "-4", "-2", "0", "0", "2", "2", "2", "0", "7", "5", "3", "3", "1", "1", "1", "3", "-1", "-1", "-1", "1", "-1" ]
[ "sign" ]
7
0
3
[ "A001511", "A001700", "A029744", "A053251", "A124754", "A344618", "A344619", "A357136", "A357182", "A357183", "A357184", "A357185", "A357621", "A357622", "A357623", "A357624", "A357625", "A357626", "A357627", "A357628", "A357630", "A357634", "A357637", "A357638", "A357639", "A357641", "A357642" ]
null
Gus Wiseman, Oct 08 2022
2022-10-08T09:39:55
oeisdata/seq/A357/A357623.seq
a70d36c8202453adc4b0fdbf6782eccb
A357624
Skew-alternating sum of the reversed n-th composition in standard order.
[ "0", "1", "2", "0", "3", "-1", "1", "-1", "4", "-2", "0", "-2", "2", "-2", "0", "0", "5", "-3", "-1", "-3", "1", "-3", "-1", "1", "3", "-3", "-1", "-1", "1", "-1", "1", "1", "6", "-4", "-2", "-4", "0", "-4", "-2", "2", "2", "-4", "-2", "0", "0", "0", "2", "2", "4", "-4", "-2", "-2", "0", "-2", "0", "2", "2", "-2", "0", "0", "2", "0", "2", "0", "7", "-5", "-3", "-5", "-1", "-5", "-3", "3", "1", "-5", "-3", "1" ]
[ "sign" ]
5
0
3
[ "A001511", "A001700", "A053251", "A124754", "A344618", "A344619", "A357136", "A357182", "A357183", "A357184", "A357185", "A357621", "A357622", "A357623", "A357624", "A357625", "A357626", "A357627", "A357628", "A357629", "A357630", "A357634", "A357637", "A357638", "A357639", "A357640", "A357641", "A357642" ]
null
Gus Wiseman, Oct 08 2022
2022-10-08T09:39:50
oeisdata/seq/A357/A357624.seq
a02fe282e5aef26431791a82037dcaa4
A357625
Numbers k such that the k-th composition in standard order has half-alternating sum 0.
[ "0", "14", "15", "44", "45", "46", "52", "53", "54", "59", "61", "152", "153", "154", "156", "168", "169", "170", "172", "179", "181", "185", "200", "201", "202", "204", "211", "213", "217", "230", "231", "234", "235", "239", "242", "243", "247", "254", "255", "560", "561", "562", "564", "568", "592", "593", "594", "596", "600", "611", "613", "617", "625", "656" ]
[ "nonn" ]
11
1
2
[ "A001511", "A053251", "A124754", "A344618", "A344619", "A357136", "A357182", "A357183", "A357184", "A357185", "A357621", "A357622", "A357623", "A357625", "A357626", "A357627", "A357628", "A357629", "A357631", "A357633", "A357635", "A357637", "A357638", "A357639", "A357641", "A357642" ]
null
Gus Wiseman, Oct 08 2022
2024-06-02T14:40:27
oeisdata/seq/A357/A357625.seq
8020bb7785cc7444e3e1fd574e4b8590
A357626
Numbers k such that the reversed k-th composition in standard order has half-alternating sum 0.
[ "0", "11", "15", "37", "38", "45", "46", "53", "54", "55", "59", "137", "138", "140", "153", "154", "156", "167", "169", "170", "171", "172", "179", "191", "201", "202", "204", "205", "206", "213", "214", "229", "230", "231", "235", "243", "247", "251", "255", "529", "530", "532", "536", "561", "562", "564", "568", "583", "587", "593", "594", "595", "596", "600" ]
[ "nonn" ]
6
1
2
[ "A001511", "A053251", "A124754", "A344618", "A344619", "A357136", "A357182", "A357183", "A357184", "A357185", "A357621", "A357622", "A357623", "A357625", "A357626", "A357627", "A357628", "A357629", "A357631", "A357633", "A357635", "A357637", "A357638", "A357639", "A357641", "A357642" ]
null
Gus Wiseman, Oct 08 2022
2022-10-08T14:16:01
oeisdata/seq/A357/A357626.seq
56136ea89cba90843aa5785cbc06d316
A357627
Numbers k such that the k-th composition in standard order has skew-alternating sum 0.
[ "0", "3", "10", "11", "15", "36", "37", "38", "43", "45", "54", "55", "58", "59", "63", "136", "137", "138", "140", "147", "149", "153", "166", "167", "170", "171", "175", "178", "179", "183", "190", "191", "204", "205", "206", "212", "213", "214", "219", "221", "228", "229", "230", "235", "237", "246", "247", "250", "251", "255", "528", "529", "530", "532", "536" ]
[ "nonn" ]
5
1
2
[ "A001511", "A001700", "A053251", "A124754", "A344618", "A344619", "A357136", "A357182", "A357185", "A357621", "A357623", "A357624", "A357625", "A357626", "A357627", "A357628", "A357630", "A357632", "A357634", "A357636", "A357637", "A357638", "A357639", "A357640", "A357641", "A357642" ]
null
Gus Wiseman, Oct 08 2022
2022-10-08T14:16:11
oeisdata/seq/A357/A357627.seq
c647e36c4cdf31d441160c5e50287135
A357628
Numbers k such that the reversed k-th composition in standard order has skew-alternating sum 0.
[ "0", "3", "10", "14", "15", "36", "43", "44", "45", "52", "54", "58", "59", "61", "63", "136", "147", "149", "152", "153", "166", "168", "170", "175", "178", "179", "181", "183", "185", "190", "200", "204", "211", "212", "213", "217", "219", "221", "228", "230", "234", "235", "237", "239", "242", "246", "247", "250", "254", "255", "528", "547", "549", "553", "560" ]
[ "nonn" ]
5
1
2
[ "A001511", "A001700", "A053251", "A124754", "A344618", "A344619", "A357136", "A357182", "A357183", "A357184", "A357185", "A357622", "A357623", "A357624", "A357625", "A357626", "A357627", "A357628", "A357632", "A357635", "A357636", "A357637", "A357638", "A357639", "A357640", "A357641", "A357642" ]
null
Gus Wiseman, Oct 08 2022
2022-10-08T14:16:15
oeisdata/seq/A357/A357628.seq
0206198a9582a3e4205f3af3e79ed46c
A357629
Half-alternating sum of the prime indices of n.
[ "0", "1", "2", "2", "3", "3", "4", "1", "4", "4", "5", "0", "6", "5", "5", "0", "7", "1", "8", "-1", "6", "6", "9", "-1", "6", "7", "2", "-2", "10", "0", "11", "1", "7", "8", "7", "-2", "12", "9", "8", "-2", "13", "-1", "14", "-3", "1", "10", "15", "2", "8", "1", "9", "-4", "16", "-1", "8", "-3", "10", "11", "17", "-3", "18", "12", "0", "2", "9", "-2", "19", "-5", "11", "0", "20", "1", "21", "13", "2", "-6" ]
[ "sign" ]
6
1
3
[ "A003963", "A053251", "A055932", "A056239", "A112798", "A316524", "A344616", "A351005", "A351006", "A357189", "A357485", "A357488", "A357621", "A357622", "A357623", "A357626", "A357629", "A357630", "A357631", "A357632", "A357633", "A357634", "A357635", "A357636", "A357637", "A357638", "A357639", "A357640", "A357641", "A357642", "A357643", "A357644" ]
null
Gus Wiseman, Oct 08 2022
2022-10-09T09:42:00
oeisdata/seq/A357/A357629.seq
f6d9bd3b7e2474b8231e19e3d4c0f1fe
A357630
Skew-alternating sum of the prime indices of n.
[ "0", "1", "2", "0", "3", "-1", "4", "-1", "0", "-2", "5", "-2", "6", "-3", "-1", "0", "7", "-3", "8", "-3", "-2", "-4", "9", "1", "0", "-5", "-2", "-4", "10", "-4", "11", "1", "-3", "-6", "-1", "0", "12", "-7", "-4", "2", "13", "-5", "14", "-5", "-3", "-8", "15", "2", "0", "-5", "-5", "-6", "16", "-1", "-2", "3", "-6", "-9", "17", "1", "18", "-10", "-4", "0", "-3", "-6", "19", "-7", "-7", "-6", "20" ]
[ "sign" ]
6
1
3
[ "A003963", "A053251", "A055932", "A056239", "A112798", "A316524", "A344616", "A351005", "A351006", "A357189", "A357485", "A357488", "A357621", "A357622", "A357623", "A357624", "A357625", "A357626", "A357629", "A357630", "A357632", "A357633", "A357634", "A357635", "A357636", "A357637", "A357638", "A357639", "A357640", "A357641", "A357642", "A357643", "A357644" ]
null
Gus Wiseman, Oct 09 2022
2022-10-09T09:41:55
oeisdata/seq/A357/A357630.seq
e40e2b70d05a57ee95f920a1c07a4b77
A357631
Numbers k such that the half-alternating sum of the prime indices of k is 0.
[ "1", "12", "16", "30", "63", "70", "81", "108", "154", "165", "192", "256", "273", "286", "300", "325", "442", "480", "561", "588", "595", "625", "646", "700", "741", "750", "874", "931", "972", "1008", "1045", "1080", "1120", "1173", "1296", "1334", "1452", "1470", "1495", "1540", "1653", "1728", "1771", "1798", "2028", "2139", "2294", "2401", "2430" ]
[ "nonn" ]
12
1
2
[ "A000290", "A003963", "A053251", "A055932", "A056239", "A112798", "A316524", "A344616", "A351005", "A351006", "A357189", "A357485", "A357488", "A357621", "A357624", "A357625", "A357626", "A357629", "A357630", "A357631", "A357632", "A357633", "A357634", "A357635", "A357636", "A357637", "A357639", "A357640", "A357641", "A357642", "A357643", "A357644" ]
null
Gus Wiseman, Oct 09 2022
2023-10-10T16:22:30
oeisdata/seq/A357/A357631.seq
2c99f48536ee69550db2076e794b5591
A357632
Numbers k such that the skew-alternating sum of the prime indices of k is 0.
[ "1", "4", "9", "16", "25", "36", "49", "64", "81", "90", "100", "121", "144", "169", "196", "210", "225", "256", "289", "324", "360", "361", "400", "441", "462", "484", "525", "529", "550", "576", "625", "676", "729", "784", "840", "841", "858", "900", "910", "961", "1024", "1089", "1155", "1156", "1225", "1296", "1326", "1369", "1440", "1444", "1521", "1600" ]
[ "nonn" ]
9
1
2
[ "A000290", "A003963", "A053251", "A055932", "A056239", "A112798", "A316524", "A344616", "A351005", "A351006", "A357189", "A357485", "A357488", "A357621", "A357626", "A357627", "A357628", "A357629", "A357630", "A357631", "A357632", "A357634", "A357635", "A357636", "A357637", "A357638", "A357639", "A357640", "A357641", "A357642", "A357643", "A357644" ]
null
Gus Wiseman, Oct 09 2022
2022-10-10T20:47:04
oeisdata/seq/A357/A357632.seq
334ca9d2e4dd20dda6009f5b36a06624
A357633
Half-alternating sum of the partition having Heinz number n.
[ "0", "1", "2", "2", "3", "3", "4", "1", "4", "4", "5", "2", "6", "5", "5", "0", "7", "3", "8", "3", "6", "6", "9", "1", "6", "7", "2", "4", "10", "4", "11", "1", "7", "8", "7", "2", "12", "9", "8", "2", "13", "5", "14", "5", "3", "10", "15", "2", "8", "5", "9", "6", "16", "1", "8", "3", "10", "11", "17", "3", "18", "12", "4", "2", "9", "6", "19", "7", "11", "6", "20", "3", "21", "13", "4", "8", "9", "7", "22", "3", "0" ]
[ "nonn" ]
5
1
3
[ "A000583", "A003963", "A053251", "A055932", "A056239", "A112798", "A316524", "A344616", "A351005", "A351006", "A357189", "A357485", "A357488", "A357621", "A357622", "A357623", "A357626", "A357629", "A357630", "A357631", "A357632", "A357633", "A357634", "A357636", "A357637", "A357638", "A357639", "A357640", "A357641", "A357642", "A357643", "A357644" ]
null
Gus Wiseman, Oct 09 2022
2022-10-09T20:25:11
oeisdata/seq/A357/A357633.seq
3020ffee122a57490556ff4b241a13fe
A357634
Skew-alternating sum of the partition having Heinz number n.
[ "0", "1", "2", "0", "3", "1", "4", "-1", "0", "2", "5", "0", "6", "3", "1", "0", "7", "-1", "8", "1", "2", "4", "9", "1", "0", "5", "-2", "2", "10", "0", "11", "1", "3", "6", "1", "0", "12", "7", "4", "2", "13", "1", "14", "3", "-1", "8", "15", "2", "0", "-1", "5", "4", "16", "-1", "2", "3", "6", "9", "17", "1", "18", "10", "0", "0", "3", "2", "19", "5", "7", "0", "20", "1", "21", "11", "-2", "6", "1", "3", "22", "3" ]
[ "sign" ]
5
1
3
[ "A003963", "A053251", "A055932", "A056239", "A112798", "A316524", "A344616", "A351005", "A351006", "A357189", "A357485", "A357488", "A357621", "A357622", "A357623", "A357624", "A357625", "A357626", "A357629", "A357630", "A357632", "A357633", "A357634", "A357635", "A357636", "A357637", "A357638", "A357639", "A357640", "A357641", "A357642", "A357643", "A357644" ]
null
Gus Wiseman, Oct 09 2022
2022-10-09T20:26:12
oeisdata/seq/A357/A357634.seq
35d1ecad0ac38f4d08d3ef6e9d9f5b8f
A357635
Numbers k such that the half-alternating sum of the partition having Heinz number k is 1.
[ "2", "8", "24", "32", "54", "128", "135", "162", "375", "384", "512", "648", "864", "875", "1250", "1715", "1944", "2048", "2160", "2592", "3773", "4374", "4802", "5000", "6000", "6144", "8192", "9317", "10368", "10935", "13122", "13824", "14000", "15000", "17303", "19208", "20000", "24167", "27440", "29282", "30375", "31104", "32768", "33750" ]
[ "nonn" ]
6
1
1
[ "A000290", "A000583", "A003963", "A035444", "A035544", "A053251", "A055932", "A056239", "A112798", "A316524", "A344616", "A345958", "A351005", "A351006", "A357621", "A357624", "A357625", "A357626", "A357629", "A357630", "A357631", "A357632", "A357633", "A357634", "A357635", "A357636", "A357637", "A357639", "A357640", "A357641", "A357642", "A357643", "A357644", "A357851" ]
null
Gus Wiseman, Oct 28 2022
2022-10-29T09:10:03
oeisdata/seq/A357/A357635.seq
8a2b3afce7cafdd99283ce2fe2a2db14
A357636
Numbers k such that the skew-alternating sum of the partition having Heinz number k is 0.
[ "1", "4", "9", "12", "16", "25", "30", "36", "49", "63", "64", "70", "81", "90", "100", "108", "121", "144", "154", "165", "169", "192", "196", "210", "225", "256", "273", "286", "289", "300", "324", "325", "360", "361", "400", "441", "442", "462", "480", "484", "525", "529", "550", "561", "576", "588", "595", "625", "646", "676", "700", "729", "741", "750", "784" ]
[ "nonn" ]
6
1
2
[ "A000290", "A000583", "A003963", "A035594", "A053251", "A055932", "A056239", "A112798", "A316524", "A344616", "A351005", "A351006", "A357189", "A357485", "A357488", "A357621", "A357626", "A357627", "A357628", "A357629", "A357630", "A357631", "A357632", "A357634", "A357636", "A357637", "A357638", "A357639", "A357640", "A357641", "A357642", "A357643", "A357644" ]
null
Gus Wiseman, Oct 09 2022
2022-10-10T20:47:00
oeisdata/seq/A357/A357636.seq
11f25e00ab9c0c54eff838eb8f100832
A357637
Triangle read by rows where T(n,k) is the number of integer partitions of n with half-alternating sum k, where k ranges from -n to n in steps of 2.
[ "1", "0", "1", "0", "0", "2", "0", "0", "1", "2", "0", "0", "1", "1", "3", "0", "0", "0", "2", "2", "3", "0", "0", "0", "0", "5", "2", "4", "0", "0", "0", "0", "2", "6", "3", "4", "0", "0", "0", "0", "2", "3", "9", "3", "5", "0", "0", "0", "0", "0", "4", "7", "10", "4", "5", "0", "0", "0", "0", "0", "0", "11", "8", "13", "4", "6", "0", "0", "0", "0", "0", "0", "4", "15", "12", "14", "5", "6", "0", "0", "0", "0", "0", "0", "3", "7", "25", "13", "17", "5", "7" ]
[ "nonn", "tabl" ]
16
0
6
[ "A000041", "A004525", "A008619", "A029862", "A035363", "A035544", "A053251", "A097805", "A344651", "A351005", "A351006", "A357136", "A357189", "A357487", "A357488", "A357621", "A357623", "A357629", "A357630", "A357631", "A357632", "A357633", "A357634", "A357637", "A357638", "A357639", "A357640", "A357641", "A357643", "A357644", "A357645", "A357646", "A357704", "A357705" ]
null
Gus Wiseman, Oct 10 2022
2022-10-12T14:19:53
oeisdata/seq/A357/A357637.seq
bb888c722279283361cae3b9786bea8f
A357638
Triangle read by rows where T(n,k) is the number of integer partitions of n with skew-alternating sum k, where k ranges from -n to n in steps of 2.
[ "1", "0", "1", "0", "1", "1", "0", "1", "1", "1", "0", "0", "3", "1", "1", "0", "0", "1", "4", "1", "1", "0", "0", "1", "4", "4", "1", "1", "0", "0", "0", "4", "5", "4", "1", "1", "0", "0", "0", "1", "10", "5", "4", "1", "1", "0", "0", "0", "1", "5", "13", "5", "4", "1", "1", "0", "0", "0", "0", "4", "13", "14", "5", "4", "1", "1", "0", "0", "0", "0", "1", "13", "17", "14", "5", "4", "1", "1" ]
[ "nonn", "tabl" ]
5
0
13
[ "A000041", "A004396", "A035363", "A035544", "A035594", "A053251", "A097805", "A146325", "A298311", "A344651", "A351005", "A351006", "A357136", "A357189", "A357486", "A357487", "A357488", "A357621", "A357623", "A357624", "A357629", "A357630", "A357631", "A357632", "A357633", "A357634", "A357636", "A357637", "A357638", "A357643", "A357644", "A357645", "A357646", "A357704", "A357705" ]
null
Gus Wiseman, Oct 10 2022
2022-10-10T20:47:17
oeisdata/seq/A357/A357638.seq
1c5a4230a40eddd09a0cd76a2795dfcb
A357639
Number of reversed integer partitions of 2n whose half-alternating sum is 0.
[ "1", "0", "2", "1", "6", "4", "15", "13", "37", "37", "86", "94", "194", "223", "416", "497", "867", "1056", "1746", "2159", "3424", "4272", "6546", "8215", "12248", "15418", "22449", "28311", "40415", "50985", "71543", "90222", "124730", "157132", "214392", "269696", "363733", "456739", "609611", "763969", "1010203", "1263248", "1656335", "2066552", "2688866" ]
[ "nonn" ]
19
0
3
[ "A000041", "A029862", "A035363", "A035444", "A035544", "A035594", "A053251", "A097805", "A316524", "A344616", "A344651", "A351005", "A351006", "A357189", "A357487", "A357488", "A357621", "A357623", "A357629", "A357630", "A357631", "A357632", "A357633", "A357634", "A357636", "A357637", "A357639", "A357640", "A357641", "A357643", "A357644", "A357645", "A357704" ]
null
Gus Wiseman, Oct 11 2022
2022-10-19T18:09:41
oeisdata/seq/A357/A357639.seq
22b987ef0b2a78e61a32cc2f891dadeb
A357640
Number of reversed integer partitions of 2n whose skew-alternating sum is 0.
[ "1", "1", "2", "3", "6", "9", "16", "24", "40", "59", "93", "136", "208", "299", "445", "632", "921", "1292", "1848", "2563", "3610", "4954", "6881", "9353", "12835", "17290", "23469", "31357", "42150", "55889", "74463", "98038", "129573", "169476", "222339", "289029", "376618", "486773", "630313", "810285", "1043123", "1334174" ]
[ "nonn" ]
16
0
3
[ "A000041", "A029862", "A035363", "A035444", "A035544", "A035594", "A053251", "A097805", "A316524", "A344616", "A344651", "A351005", "A351006", "A357136", "A357189", "A357487", "A357488", "A357621", "A357623", "A357629", "A357630", "A357631", "A357632", "A357633", "A357634", "A357636", "A357637", "A357638", "A357639", "A357640", "A357641", "A357643", "A357644", "A357645", "A357704" ]
null
Gus Wiseman, Oct 11 2022
2022-10-19T18:49:38
oeisdata/seq/A357/A357640.seq
2389779d4a15475325e86e4cd4986c95
A357641
Number of integer compositions of 2n whose half-alternating sum is 0.
[ "1", "0", "2", "8", "28", "104", "396", "1504", "5720", "21872", "83980", "323344", "1248072", "4828784", "18721080", "72711552", "282861360", "1101980000", "4298748300", "16789002736", "65641204200", "256895795312", "1006308200040", "3945185586368", "15478849767888", "60774329914144", "238775589937976" ]
[ "nonn" ]
15
0
3
[ "A000583", "A001511", "A001700", "A035363", "A053251", "A088218", "A124754", "A344618", "A344619", "A357136", "A357182", "A357621", "A357622", "A357625", "A357626", "A357627", "A357628", "A357629", "A357631", "A357633", "A357637", "A357638", "A357639", "A357641", "A357642" ]
null
Gus Wiseman, Oct 12 2022
2022-10-19T19:04:07
oeisdata/seq/A357/A357641.seq
76f7ce9f93e3788b3dbc059dd82c8ce6
A357642
Number of even-length integer compositions of 2n whose half-alternating sum is 0.
[ "1", "0", "1", "4", "13", "48", "186", "712", "2717", "10432", "40222", "155384", "601426", "2332640", "9063380", "35269392", "137438685", "536257280", "2094786870", "8191506136", "32063203590", "125613386912", "492516592620", "1932569186288", "7588478653938", "29816630378368", "117226929901676", "461151757861552" ]
[ "nonn" ]
13
0
4
[ "A000583", "A000984", "A001511", "A001700", "A035363", "A053251", "A088218", "A110145", "A124754", "A344618", "A344619", "A357136", "A357182", "A357621", "A357622", "A357625", "A357626", "A357627", "A357628", "A357629", "A357631", "A357633", "A357637", "A357638", "A357639", "A357642" ]
null
Gus Wiseman, Oct 12 2022
2022-10-13T06:36:31
oeisdata/seq/A357/A357642.seq
e4869dbf34856038a300e925251f38cf
A357643
Number of integer compositions of n into parts that are alternately equal and unequal.
[ "1", "1", "2", "1", "3", "3", "5", "5", "9", "7", "17", "14", "28", "25", "49", "42", "87", "75", "150", "132", "266", "226", "466", "399", "810", "704", "1421", "1223", "2488", "2143", "4352", "3759", "7621", "6564", "13339", "11495", "23339", "20135", "40852", "35215", "71512", "61639", "125148", "107912", "219040", "188839", "383391", "330515", "670998" ]
[ "nonn" ]
16
0
3
[ "A001590", "A003242", "A011782", "A016116", "A029862", "A035457", "A035544", "A097805", "A122129", "A122134", "A122135", "A351003", "A351004", "A351005", "A351006", "A351007", "A351010", "A357136", "A357621", "A357623", "A357641", "A357643", "A357644", "A357645", "A357646" ]
null
Gus Wiseman, Oct 12 2022
2024-06-01T05:40:07
oeisdata/seq/A357/A357643.seq
6b0849a42d979ccf9f1654cc42329045
A357644
Number of integer compositions of n into parts that are alternately unequal and equal.
[ "1", "1", "1", "3", "4", "7", "8", "13", "17", "25", "30", "44", "58", "77", "98", "142", "176", "245", "311", "426", "548", "758", "952", "1319", "1682", "2308", "2934", "4059", "5132", "7087", "9008", "12395", "15757", "21728", "27552", "38019", "48272", "66515", "84462", "116467", "147812", "203825", "258772", "356686", "452876", "624399", "792578" ]
[ "nonn" ]
10
0
4
[ "A000213", "A001590", "A003242", "A011782", "A027383", "A029862", "A035457", "A035544", "A097805", "A122129", "A122134", "A122135", "A351003", "A351004", "A351005", "A351006", "A351007", "A351010", "A357136", "A357621", "A357623", "A357641", "A357643", "A357644", "A357645", "A357646" ]
null
Gus Wiseman, Oct 14 2022
2022-10-19T18:18:06
oeisdata/seq/A357/A357644.seq
5386d6872c86f460f9952d38eae258a0
A357645
Triangle read by rows where T(n,k) is the number of integer compositions of n with half-alternating sum k, where k ranges from -n to n in steps of 2.
[ "1", "0", "1", "0", "0", "2", "0", "0", "1", "3", "0", "0", "2", "2", "4", "0", "0", "3", "5", "3", "5", "0", "0", "4", "8", "10", "4", "6", "0", "0", "5", "11", "18", "18", "5", "7", "0", "0", "6", "14", "28", "36", "30", "6", "8", "0", "0", "7", "17", "41", "63", "65", "47", "7", "9", "0", "0", "8", "20", "58", "104", "126", "108", "70", "8", "10", "0", "0", "9", "23", "80", "164", "230", "230", "168", "100", "9", "11" ]
[ "nonn", "tabl" ]
5
0
6
[ "A011782", "A029862", "A035363", "A035544", "A097805", "A177787", "A344651", "A351005", "A351006", "A357136", "A357621", "A357623", "A357629", "A357630", "A357631", "A357633", "A357634", "A357637", "A357638", "A357639", "A357641", "A357643", "A357644", "A357645", "A357646", "A357704", "A357705" ]
null
Gus Wiseman, Oct 12 2022
2022-10-12T09:00:48
oeisdata/seq/A357/A357645.seq
c3f60a64dfa3b44849ff5e6148094903
A357646
Triangle read by rows where T(n,k) is the number of integer compositions of n with skew-alternating sum k, where k ranges from -n to n in steps of 2.
[ "1", "0", "1", "0", "1", "1", "0", "2", "1", "1", "0", "3", "3", "1", "1", "0", "4", "5", "5", "1", "1", "0", "5", "7", "10", "8", "1", "1", "0", "6", "9", "17", "18", "12", "1", "1", "0", "7", "11", "27", "35", "29", "17", "1", "1", "0", "8", "13", "41", "63", "63", "43", "23", "1", "1", "0", "9", "15", "60", "106", "126", "104", "60", "30", "1", "1", "0", "10", "17", "85", "168", "232", "230", "162", "80", "38", "1", "1" ]
[ "nonn", "tabl" ]
5
0
8
[ "A001700", "A011782", "A029862", "A035363", "A035544", "A097805", "A177787", "A344651", "A357136", "A357621", "A357623", "A357630", "A357631", "A357634", "A357637", "A357638", "A357639", "A357641", "A357643", "A357644", "A357645", "A357646", "A357704", "A357705" ]
null
Gus Wiseman, Oct 12 2022
2022-10-12T19:44:46
oeisdata/seq/A357/A357646.seq
f1f9fb95fe16cb26d68c36a68ef83326
A357647
a(n) is the number of free unholey polyominoes of n cells with 90-degree rotational symmetry and no other.
[ "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "2", "2", "0", "0", "7", "7", "0", "0", "22", "24", "0", "0", "71", "82", "0", "0", "239", "280", "0", "0", "817", "970", "0", "0", "2841", "3403", "0", "0", "10027", "12064", "0", "0", "35800", "43193", "0", "0", "129007", "156011", "0", "0", "468541", "567664", "0", "0", "1713174" ]
[ "nonn" ]
9
1
12
[ "A000104", "A144553", "A357647" ]
null
John Mason, Oct 10 2022
2022-10-10T20:12:23
oeisdata/seq/A357/A357647.seq
50ac0301ed443b362a85469fe1033789
A357648
Number of polyominoes with n cells that have the symmetry group D_8 and are without holes.
[ "1", "0", "0", "1", "1", "0", "0", "0", "2", "0", "0", "1", "2", "0", "0", "1", "3", "0", "0", "1", "5", "0", "0", "2", "8", "0", "0", "2", "13", "0", "0", "3", "20", "0", "0", "5", "33", "0", "0", "6", "55", "0", "0", "10", "93", "0", "0", "13", "157", "0", "0", "22", "268", "0", "0", "30", "461", "0", "0", "51", "801", "0", "0", "71", "1396", "0", "0", "124", "2459", "0", "0", "175", "4329", "0", "0", "317", "7696" ]
[ "nonn" ]
6
1
9
[ "A000104", "A142886", "A357648" ]
null
John Mason, Oct 10 2022
2022-10-10T04:34:04
oeisdata/seq/A357/A357648.seq
31de7366c4aa94c65100364da12169a1
A357649
Expansion of e.g.f. cosh( (exp(3*x) - 1)/3 ).
[ "1", "0", "1", "9", "64", "435", "3097", "24822", "232759", "2517345", "30070954", "382827225", "5110770205", "71421582024", "1049487311485", "16286699945853", "267145966335088", "4616924929100535", "83622792656855125", "1578916985654901366", "30957723637379211115", "628927539690331202661" ]
[ "nonn" ]
14
0
4
[ "A009153", "A024430", "A356572", "A357649", "A357650" ]
null
Seiichi Manyama, Oct 07 2022
2022-10-07T15:47:13
oeisdata/seq/A357/A357649.seq
896c663702ffee1d6ca3fa5e2c021807
A357650
Expansion of e.g.f. cosh( (exp(4*x) - 1)/4 ).
[ "1", "0", "1", "12", "113", "1000", "8977", "86996", "959905", "12303888", "179038689", "2840696540", "47684181393", "835731314808", "15277172343409", "292597596283684", "5900038421042753", "125488177929542944", "2809541905807203009", "65903118624174027436", "1610968753088423886257" ]
[ "nonn" ]
12
0
4
[ "A009153", "A024430", "A357617", "A357649", "A357650" ]
null
Seiichi Manyama, Oct 07 2022
2022-10-07T15:46:57
oeisdata/seq/A357/A357650.seq
3e7f7eb35fdbb6994a877923b78a00b1
A357651
Sliding numbers which are products of two distinct primes.
[ "65", "133", "205", "254", "502", "785", "2005", "10001", "15689", "16265", "20005", "31282", "79405", "100001", "156314", "390881", "1000001", "3906506", "10000001", "100000001", "244144721", "5000000002", "6103532009", "152587956161", "762939584197", "3814699887065", "19073486852413", "38146972918394", "200000000000005", "10000000000000000001" ]
[ "nonn", "base" ]
14
1
1
[ "A006881", "A103182", "A357651" ]
null
Massimo Kofler, Oct 07 2022
2022-10-09T15:45:51
oeisdata/seq/A357/A357651.seq
68127d8cb16497d2e2159efbf02bcf1f
A357652
Number of pairs of Dyck paths of semilength n such that the midpoint of the first is not below the midpoint of the second.
[ "1", "1", "3", "21", "147", "1323", "12618", "131085", "1430187", "16297347", "191987562", "2325379147", "28821761290", "364290802138", "4682375323044", "61067639131197", "806671205158587", "10776418254992139", "145413196382253114", "1979833455619072515", "27174458892459331530", "375722890152963114330" ]
[ "nonn" ]
12
0
3
[ "A000108", "A001246", "A129123", "A355481", "A357652" ]
null
Alois P. Heinz, Oct 07 2022
2022-10-12T15:22:54
oeisdata/seq/A357/A357652.seq
ffd168063e4751d10d3a8106571778d2
A357653
Number of walks on four-dimensional lattice from (n,n,n,n) to (0,0,0,0) using steps that decrease the Euclidean distance to the origin and that change each coordinate by 1 or by -1.
[ "1", "1", "49", "781", "221353", "28704961", "6416941789", "1600436821729", "487955996194681", "163694597214638617", "62083509504427287565", "25552605919005414839089", "11415972657891136715599597", "5444030337763685110787232601", "2758095341306366256765459135265" ]
[ "nonn", "walk" ]
12
0
3
[ "A348201", "A357653" ]
null
Alois P. Heinz, Oct 07 2022
2022-10-13T04:44:09
oeisdata/seq/A357/A357653.seq
3b39beb8736624b91256c9a8b4a0e012
A357654
Number of lattice paths from (0,0) to (i,n-2*i) that do not go above the diagonal x=y using steps in {(1,0), (0,1)}.
[ "1", "0", "1", "1", "1", "2", "3", "3", "6", "9", "10", "19", "29", "34", "63", "97", "118", "215", "333", "416", "749", "1165", "1485", "2650", "4135", "5355", "9490", "14845", "19473", "34318", "53791", "71313", "125104", "196417", "262735", "459152", "721887", "973027", "1694914", "2667941", "3619955", "6287896", "9907851", "13521307", "23429158" ]
[ "nonn", "walk" ]
14
0
6
[ "A120730", "A165407", "A357654", "A357655" ]
null
Alois P. Heinz, Oct 07 2022
2022-11-08T01:47:04
oeisdata/seq/A357/A357654.seq
bc90956a23553a8e457e5cfb80686981
A357655
Total number of nodes summed over all lattice paths from (0,0) to (i,n-2*i) that do not go above the diagonal x=y using steps in {(1,0), (0,1)}.
[ "1", "0", "2", "3", "3", "8", "14", "15", "35", "59", "69", "147", "245", "300", "608", "1005", "1269", "2489", "4091", "5280", "10120", "16565", "21735", "40950", "66820", "88815", "165125", "268785", "361005", "664108", "1078904", "1461609", "2665617", "4323643", "5899917", "10682712", "17304516", "23759955", "42759385", "69187281" ]
[ "nonn", "walk" ]
13
0
3
[ "A357654", "A357655" ]
null
Alois P. Heinz, Oct 07 2022
2023-05-27T09:13:13
oeisdata/seq/A357/A357655.seq
503a9a18ea8169d8b1ac400dff175528
A357656
a(n) is a lower bound for the largest Hamming weight of squares with exactly n binary zeros.
[ "1", "0", "13", "8", "13", "16", "37", "38", "44" ]
[ "nonn", "base", "hard", "more" ]
7
0
3
[ "A000120", "A000290", "A159918", "A230097", "A356878", "A357304", "A357305", "A357656", "A357657" ]
null
Karl-Heinz Hofmann and Hugo Pfoertner, Oct 07 2022
2022-10-13T15:28:39
oeisdata/seq/A357/A357656.seq
6a4377ef4bd34772ff26eb12067e63ce
A357657
a(n) is a lower bound for the square root of the maximum square with exactly n zeros in its binary representation.
[ "1", "0", "181", "45", "362", "1241", "2965685", "5931189", "57804981" ]
[ "nonn", "base", "hard", "more" ]
6
0
3
[ "A000120", "A000290", "A159918", "A230097", "A356838", "A357304", "A357305", "A357656", "A357657", "A357753", "A357754" ]
null
Karl-Heinz Hofmann and Hugo Pfoertner, Oct 08 2022
2022-10-13T15:28:46
oeisdata/seq/A357/A357657.seq
ce6625db2f157ae4d7e7939596cb655d
A357658
a(n) is the maximum Hamming weight of squares k^2 in the range 2^n <= k^2 < 2^(n+1).
[ "1", "2", "3", "3", "5", "4", "6", "6", "8", "8", "9", "9", "13", "11", "13", "12", "14", "15", "16", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "25", "26", "27", "28", "29", "30", "31", "31", "34", "33", "34", "37", "37", "38", "38", "39", "39", "41", "41", "42", "44", "44", "44", "46", "47", "47", "49", "50", "51", "52", "52", "53", "54", "55", "55", "57", "57", "58", "59", "62", "63" ]
[ "nonn", "base" ]
44
2
2
[ "A000120", "A000290", "A356878", "A357304", "A357658", "A357659", "A357660", "A357753", "A357754" ]
null
Hugo Pfoertner, Oct 09 2022
2022-12-21T20:18:06
oeisdata/seq/A357/A357658.seq
b5e1bfc65cb6f567126b31ea883ee98e
A357659
a(n) is the least k such that k^2 has a maximal Hamming weight A357658(n) in the range 2^n <= k^2 < 2^(n+1).
[ "2", "3", "5", "7", "11", "13", "21", "27", "45", "53", "75", "101", "181", "217", "362", "437", "627", "923", "1241", "1619", "2505", "3915", "5221", "6475", "11309", "15595", "19637", "31595", "44491", "61029", "69451", "113447", "185269", "244661", "357081", "453677", "642119", "980853", "1380917", "1961706", "2965685", "3923411", "5931189", "8096813" ]
[ "nonn", "base" ]
29
2
1
[ "A000120", "A000290", "A357658", "A357659", "A357660" ]
null
Hugo Pfoertner, Oct 09 2022
2022-12-21T12:53:15
oeisdata/seq/A357/A357659.seq
bb084ca4b250d7bdd5fa067b3d0f34f4
A357660
a(n) is the largest k such that k^2 has a maximal Hamming weight A357658(n) in the range 2^n <= k^2 < 2^(n+1).
[ "2", "3", "5", "7", "11", "15", "21", "27", "45", "53", "89", "117", "181", "235", "362", "491", "723", "949", "1241", "1773", "2891", "3915", "5747", "7093", "11309", "16203", "19637", "31595", "44491", "64747", "86581", "113447", "185269", "244661", "357081", "453677", "738539", "980853", "1481453", "2079669", "2965685", "3923411", "5931189", "8222581" ]
[ "nonn", "base" ]
29
2
1
[ "A000120", "A000290", "A357658", "A357659", "A357660" ]
null
Hugo Pfoertner, Oct 09 2022
2022-12-21T12:53:10
oeisdata/seq/A357/A357660.seq
500b0f2c7f5f5ad9bcea65f60e8ef11d
A357661
Expansion of e.g.f. cosh( (exp(2*x) - 1)/sqrt(2) ).
[ "1", "0", "2", "12", "60", "320", "2040", "15568", "133648", "1230336", "11962400", "123144384", "1349008320", "15731096576", "194349866880", "2527082917120", "34392647418112", "488243791183872", "7216792525799936", "110936087161801728", "1771199461131500544", "29324602146652307456" ]
[ "nonn" ]
15
0
3
[ "A009153", "A024430", "A264036", "A357661", "A357662", "A357663", "A357664" ]
null
Seiichi Manyama, Oct 07 2022
2025-03-23T17:04:54
oeisdata/seq/A357/A357661.seq
05f345b0aa97e56b81733eadd697a7e9
A357662
Expansion of e.g.f. cosh( (exp(3*x) - 1)/sqrt(3) ).
[ "1", "0", "3", "27", "198", "1485", "12825", "132678", "1582497", "20603727", "284290560", "4132840239", "63571690485", "1038868740000", "18022911716439", "330305863479615", "6355242571945878", "127721845479277737", "2672729031195365949", "58142565625982730462", "1313557910179640120061" ]
[ "nonn" ]
11
0
3
[ "A024430", "A357615", "A357649", "A357661", "A357662", "A357663", "A357665" ]
null
Seiichi Manyama, Oct 07 2022
2022-10-08T08:33:03
oeisdata/seq/A357/A357662.seq
20705a23931a12dcb204b5ecc46a987b
A357663
Expansion of e.g.f. cosh( (exp(4*x) - 1)/2 ).
[ "1", "0", "4", "48", "464", "4480", "48448", "621824", "9320704", "154890240", "2746131456", "51237908480", "1007228375040", "20965557829632", "463091379159040", "10826828061147136", "266438312153120768", "6861616219559034880", "184128217520198123520", "5135753969867535941632" ]
[ "nonn" ]
11
0
3
[ "A024430", "A065143", "A357650", "A357661", "A357662", "A357663", "A357666" ]
null
Seiichi Manyama, Oct 07 2022
2022-10-08T08:33:21
oeisdata/seq/A357/A357663.seq
8f37b93f73e1393dc6da67cd3fe7f93a
A357664
Expansion of e.g.f. sinh( (exp(2*x) - 1)/sqrt(2) )/sqrt(2).
[ "0", "1", "2", "6", "32", "220", "1592", "11944", "96000", "847120", "8209952", "86020704", "958326272", "11243157952", "138464594816", "1789358629504", "24250275913728", "344002396594432", "5092763802452480", "78443316497892864", "1253887341918199808", "20761127890765634560" ]
[ "nonn" ]
10
0
3
[ "A009599", "A024429", "A264037", "A357661", "A357664", "A357665", "A357666" ]
null
Seiichi Manyama, Oct 07 2022
2022-10-08T08:33:07
oeisdata/seq/A357/A357664.seq
4a77ec40a3b9cab6f7789af4d317c551
A357665
Expansion of e.g.f. sinh( (exp(3*x) - 1)/sqrt(3) )/sqrt(3).
[ "0", "1", "3", "12", "81", "765", "7938", "85239", "963819", "11801862", "158533443", "2320621569", "36425289816", "604576791405", "10532817901791", "192197187209484", "3673078679995677", "73486862051182425", "1536507360834633666", "33482575797899354235", "758209049155176114807" ]
[ "nonn" ]
10
0
3
[ "A024429", "A356572", "A357572", "A357662", "A357664", "A357665", "A357666" ]
null
Seiichi Manyama, Oct 07 2022
2022-10-08T08:33:11
oeisdata/seq/A357/A357665.seq
a9020e4ec764640c014a937a3791ed05
A357666
Expansion of e.g.f. sinh( (exp(4*x) - 1)/2 )/2.
[ "0", "1", "4", "20", "160", "1872", "25024", "348224", "5055488", "78571776", "1332573184", "24695206912", "493816963072", "10492449771520", "234399640633344", "5480635606908928", "134015043318054912", "3427700843478056960", "91642829715498336256", "2556218693498006929408" ]
[ "nonn" ]
11
0
3
[ "A024429", "A357598", "A357617", "A357663", "A357664", "A357665", "A357666" ]
null
Seiichi Manyama, Oct 07 2022
2022-10-08T08:33:15
oeisdata/seq/A357/A357666.seq
a29b04843a36b4b052e3cbdb745b1568
A357667
Expansion of e.g.f. cosh( 3 * (exp(x) - 1) ).
[ "1", "0", "9", "27", "144", "945", "6273", "44226", "339399", "2796795", "24387786", "223853355", "2159078445", "21827316888", "230536050165", "2536213188519", "28994911890048", "343806474384045", "4220933769308205", "53566838971016418", "701650841036287275", "9473067208871584407" ]
[ "nonn" ]
29
0
3
[ "A024430", "A027710", "A065143", "A264036", "A357615", "A357649", "A357667", "A357668", "A357681" ]
null
Seiichi Manyama, Oct 08 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357667.seq
086a1d9a927d3866a01be1d972c8e97d
A357668
Expansion of e.g.f. sinh( 3 * (exp(x) - 1) )/3.
[ "0", "1", "1", "10", "55", "307", "2026", "14779", "114157", "933616", "8110261", "74525167", "719925328", "7279859485", "76855303981", "845280487018", "9663800287483", "114601481983855", "1407040763488354", "17856103120048783", "233883061849700137", "3157648445216335528", "43887908697233605489" ]
[ "nonn" ]
25
0
4
[ "A024429", "A027710", "A264037", "A356572", "A357572", "A357598", "A357667", "A357668" ]
null
Seiichi Manyama, Oct 08 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357668.seq
5aa8684e8a4f8b06b494fde863525049
A357669
a(n) is the number of divisors of the powerful part of n.
[ "1", "1", "1", "3", "1", "1", "1", "4", "3", "1", "1", "3", "1", "1", "1", "5", "1", "3", "1", "3", "1", "1", "1", "4", "3", "1", "4", "3", "1", "1", "1", "6", "1", "1", "1", "9", "1", "1", "1", "4", "1", "1", "1", "3", "3", "1", "1", "5", "3", "3", "1", "3", "1", "4", "1", "4", "1", "1", "1", "3", "1", "1", "3", "7", "1", "1", "1", "3", "1", "1", "1", "12", "1", "1", "3", "3", "1", "1", "1", "5", "5", "1", "1", "3", "1", "1", "1" ]
[ "nonn", "easy", "mult" ]
12
1
4
[ "A000005", "A001694", "A003557", "A005117", "A056671", "A057521", "A064549", "A295294", "A357669" ]
null
Amiram Eldar, Oct 08 2022
2023-09-10T04:51:38
oeisdata/seq/A357/A357669.seq
5807b1e152c6a3ed82eba0bafbf9dbcb
A357670
Sliding numbers which are products of three distinct primes.
[ "70", "110", "290", "1001", "1010", "1258", "3157", "3445", "5002", "6266", "6410", "50002", "1958245", "2000005", "9766649", "9775865", "20000005", "48830173", "200000005", "488283298", "2000000005", "2441410346", "6103679465", "10000000001", "12207039442", "30517905805", "50000000002", "61035172634", "152588545985", "200000000005", "305175814018" ]
[ "nonn", "base" ]
16
1
1
[ "A007304", "A103182", "A357670" ]
null
Massimo Kofler, Oct 08 2022
2022-10-09T15:45:59
oeisdata/seq/A357/A357670.seq
099dd05d00878ea7bf7173ab0e8ac417
A357671
a(n) = Sum_{k = 0..n} ( binomial(n+k-1,k) + binomial(n+k-1,k)^2 ).
[ "2", "4", "20", "166", "1812", "22504", "297362", "4067298", "56897300", "809019580", "11649254520", "169444978124", "2485270719570", "36707044807996", "545386321069862", "8144809732228666", "122177690210103060", "1839933274439787940", "27804610626798500372", "421476329345312885304", "6406685025104178888312" ]
[ "nonn", "easy" ]
26
0
1
[ "A000984", "A333592", "A357509", "A357565", "A357566", "A357671", "A357672", "A357673", "A357674" ]
null
Peter Bala, Oct 10 2022
2023-05-09T15:36:44
oeisdata/seq/A357/A357671.seq
a09866f113c72acd35e25b8e8ddc28ba
A357672
a(n) = Sum_{k = 0..n} binomial(n+k-1,k) * Sum_{k = 0..n} binomial(n+k-1,k)^2.
[ "1", "4", "84", "2920", "121940", "5607504", "273908712", "13947188112", "732102614100", "39332168075200", "2152235533317584", "119531412173662944", "6720552415489860584", "381775182057562837600", "21879043278489630349200", "1263402662473729731877920", "73438613319490294002441300", "4293679728171938162242298400" ]
[ "nonn", "easy" ]
27
0
2
[ "A000984", "A333592", "A357565", "A357566", "A357671", "A357672", "A357673", "A357674" ]
null
Peter Bala, Oct 10 2022
2023-08-02T07:18:43
oeisdata/seq/A357/A357672.seq
45418f9eb8df11f7e6eea522fad939cf
A357673
a(n) = 4*Sum_{k = 0..2*n} binomial(n+k-1,k) + 3*Sum_{k = 0..2*n} binomial(n+k-1,k)^2.
[ "7", "21", "225", "5124", "162657", "5812521", "219004812", "8516056500", "338508840801", "13679415485805", "559978704877725", "23162632151271480", "966309241173439500", "40602415885424806824", "1716435895297948558812", "72941388509291664563124", "3113826813351114598588257", "133458673478315967012049245" ]
[ "nonn", "easy" ]
19
0
1
[ "A005809", "A357509", "A357565", "A357566", "A357671", "A357672", "A357673", "A357674" ]
null
Peter Bala, Oct 11 2022
2022-10-29T15:40:24
oeisdata/seq/A357/A357673.seq
7f3482cdd0d47228f88006c2b4909e5c
A357674
a(n) = ( Sum_{k = 0..2*n} binomial(n+k-1,k) )^4 * ( Sum_{k = 0..2*n} binomial(n+k-1,k)^2 )^3.
[ "1", "2187", "8422734375", "202402468703748096", "9223976224194016590174375", "587835594121137662072707812564687", "46157429480574073282465608886521546620928", "4181198339699286332943143923058721957212160000000", "420336565507755143573799144638372909582306681004894518439" ]
[ "nonn", "easy" ]
13
0
2
[ "A005809", "A357565", "A357566", "A357671", "A357672", "A357673", "A357674" ]
null
Peter Bala, Oct 11 2022
2022-10-28T09:56:59
oeisdata/seq/A357/A357674.seq
89c8d0e8a56f7c08a75984761ab2ec47
A357675
Smallest m such that A357477(m) = n.
[ "3", "2", "1", "31", "34", "19", "77", "67", "154", "218", "251", "653", "809", "1217", "1289", "802", "601", "3011", "1951", "806", "7204", "3345", "5612", "2890", "4876", "15888", "6502", "4340", "651", "14581", "7040", "14134", "14128", "652", "33996", "42076", "30882", "8332", "77007", "11672", "25004", "82416", "101477", "7051", "154058", "101536", "83982", "101154", "107691" ]
[ "nonn" ]
8
1
1
[ "A357477", "A357675" ]
null
Jake M. Gotlieb, Oct 08 2022
2022-12-02T12:32:36
oeisdata/seq/A357/A357675.seq
d19e829e6a5fbcec8a0cacd18cddbeaa
A357676
Indices at which record high values in A357477 appear.
[ "1", "19", "67", "154", "218", "251", "601", "651", "652", "7051", "17001", "101157", "555039", "971160", "1240273", "6191735", "81174469", "84349567", "131625552", "214344967", "214345119", "3974507614", "5446707884", "5574291825", "41016920663", "69752538433" ]
[ "nonn", "hard", "more" ]
11
1
2
[ "A357477", "A357676" ]
null
Jake M. Gotlieb, Oct 08 2022
2023-01-03T06:19:43
oeisdata/seq/A357/A357676.seq
e2108cc7d913f949e641b5e0445f11d6
A357677
Powers of either 3 or 5 or 7 (and 0).
[ "0", "1", "3", "5", "7", "9", "25", "27", "49", "81", "125", "243", "343", "625", "729", "2187", "2401", "3125", "6561", "15625", "16807", "19683", "59049", "78125", "117649", "177147", "390625", "531441", "823543", "1594323", "1953125", "4782969", "5764801", "9765625", "14348907", "40353607", "43046721", "48828125", "129140163" ]
[ "nonn", "easy" ]
24
1
3
[ "A000244", "A000351", "A000420", "A357677" ]
null
Shreevatsa R, Oct 08 2022
2022-11-11T19:41:41
oeisdata/seq/A357/A357677.seq
3151bdd68fd217bef633459769ded494
A357678
Numbers k equal to the integer log of the sum of k and its digit reversal.
[ "8", "17", "107" ]
[ "nonn", "base", "bref", "more" ]
13
1
1
[ "A001414", "A004086", "A056964", "A357678" ]
null
J. M. Bergot and Robert Israel, Oct 08 2022
2022-10-09T20:32:19
oeisdata/seq/A357/A357678.seq
3a61d9c69218f64a2c20e725dc6f8550
A357679
a(n) = prime(n)*(prime(n-1) + prime(n+1)).
[ "21", "50", "112", "220", "364", "544", "760", "1104", "1566", "2046", "2664", "3280", "3784", "4512", "5618", "6726", "7686", "8844", "9940", "10950", "12324", "13944", "16020", "18430", "20200", "21424", "22684", "23980", "26668", "30988", "34584", "36990", "39754", "43210", "46206", "49298", "52812", "56112", "59858", "63366", "66970", "71434", "74884", "77224", "81192" ]
[ "nonn", "easy" ]
63
2
1
[ "A000040", "A006094", "A048448", "A338529", "A357679" ]
null
Saish S. Kambali, Oct 09 2022
2023-02-08T07:21:01
oeisdata/seq/A357/A357679.seq
b308b0823c4ec7a8db37c61961d75cee
A357680
a(n) is the number of primes that can be written as +-1! +- 2! +- 3! +- ... +- n!.
[ "0", "1", "3", "4", "7", "11", "16", "29", "42", "72", "121", "191", "367", "693", "1215", "2221", "4116", "7577", "13900", "25634", "48322", "90046", "169016", "317819", "600982", "1138049", "2158939", "4103414", "7818761", "14923641", "28534404", "54624906", "104786140", "201233500", "386914300", "744876280", "1435592207" ]
[ "nonn" ]
49
1
3
[ "A000142", "A059590", "A089359", "A357680" ]
null
Zhining Yang, Oct 09 2022
2022-11-22T23:07:36
oeisdata/seq/A357/A357680.seq
4288dd1dadecbb691241ea637cfaf1e5
A357681
Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. cosh( sqrt(k) * (exp(x) - 1) ).
[ "1", "1", "0", "1", "0", "0", "1", "0", "1", "0", "1", "0", "2", "3", "0", "1", "0", "3", "6", "8", "0", "1", "0", "4", "9", "18", "25", "0", "1", "0", "5", "12", "30", "70", "97", "0", "1", "0", "6", "15", "44", "135", "330", "434", "0", "1", "0", "7", "18", "60", "220", "705", "1694", "2095", "0", "1", "0", "8", "21", "78", "325", "1228", "3906", "9202", "10707", "0", "1", "0", "9", "24", "98", "450", "1905", "7196", "22953", "53334", "58194", "0" ]
[ "nonn", "tabl" ]
26
0
13
[ "A000007", "A024430", "A065143", "A264036", "A292860", "A357615", "A357667", "A357681", "A357682" ]
null
Seiichi Manyama, Oct 09 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357681.seq
7d614fe0dbd95dceafaeba5b26844224
A357682
a(n) = Sum_{k=0..floor(n/2)} n^k * Stirling2(n,2*k).
[ "1", "0", "2", "9", "44", "325", "2742", "24794", "250168", "2796795", "33842610", "439337085", "6100179780", "90139379928", "1409779442190", "23242554452745", "402652762232048", "7308371248274949", "138605556986785674", "2740167375732394378", "56350604098768558140", "1203156656491936711635" ]
[ "nonn" ]
21
0
3
[ "A242817", "A357681", "A357682", "A357683" ]
null
Seiichi Manyama, Oct 09 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357682.seq
0e44903385e0ab026be4d6d71a50a429
A357683
a(n) = Sum_{k=0..floor(n/2)} n^k * |Stirling1(n,2*k)|.
[ "1", "0", "2", "9", "60", "500", "4920", "55566", "706720", "9979200", "154706760", "2609691700", "47547916416", "929943488448", "19421810408000", "431196538865400", "10137091700736000", "251485260368396288", "6563768030597826720", "179746132716715050000", "5152012082327932518400" ]
[ "nonn" ]
18
0
3
[ "A105752", "A263687", "A357683" ]
null
Seiichi Manyama, Oct 09 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357683.seq
843022cf23a6b0089ce25261a665037d
A357684
The squarefree part (A007913) of numbers whose squarefree part is a unitary divisor (A335275).
[ "1", "2", "3", "1", "5", "6", "7", "1", "10", "11", "3", "13", "14", "15", "1", "17", "2", "19", "5", "21", "22", "23", "1", "26", "7", "29", "30", "31", "33", "34", "35", "1", "37", "38", "39", "41", "42", "43", "11", "5", "46", "47", "3", "1", "2", "51", "13", "53", "55", "57", "58", "59", "15", "61", "62", "7", "1", "65", "66", "67", "17", "69", "70", "71", "73", "74", "3", "19", "77", "78", "79" ]
[ "nonn" ]
13
1
2
[ "A000290", "A005117", "A007913", "A008833", "A065465", "A069891", "A335275", "A357684" ]
null
Amiram Eldar, Oct 09 2022
2022-10-12T05:22:26
oeisdata/seq/A357/A357684.seq
5ffd884e6236aa515c0cd38677439a40
A357685
Numbers k such that A293228(k) > k.
[ "30", "42", "60", "66", "70", "78", "84", "102", "114", "132", "138", "140", "156", "174", "186", "204", "210", "222", "228", "246", "258", "276", "282", "318", "330", "348", "354", "366", "372", "390", "402", "420", "426", "438", "444", "462", "474", "492", "498", "510", "516", "534", "546", "564", "570", "582", "606", "618", "636", "642", "654", "660", "678", "690" ]
[ "nonn" ]
10
1
1
[ "A005101", "A005117", "A034683", "A064597", "A087248", "A129575", "A129656", "A292982", "A293228", "A348274", "A348604", "A357685", "A357686" ]
null
Amiram Eldar, Oct 09 2022
2022-10-12T04:34:49
oeisdata/seq/A357/A357685.seq
1e8f5129aa0f353456f3ed72ad82ba8b
A357686
Nonsquarefree numbers k such that A293228(k) > k.
[ "60", "84", "132", "140", "156", "204", "228", "276", "348", "372", "420", "444", "492", "516", "564", "636", "660", "708", "732", "780", "804", "852", "876", "924", "948", "996", "1020", "1068", "1092", "1140", "1164", "1212", "1236", "1284", "1308", "1356", "1380", "1428", "1524", "1540", "1572", "1596", "1644", "1668", "1716", "1740", "1788", "1812", "1820" ]
[ "nonn" ]
9
1
1
[ "A005101", "A013929", "A087248", "A243128", "A357685", "A357686" ]
null
Amiram Eldar, Oct 09 2022
2022-10-12T04:31:47
oeisdata/seq/A357/A357686.seq
b8c001a1da040da8634878e9babbb76b
A357687
Nonsquarefree numbers k such that A048250(k) > 2*k.
[ "401120980260", "14841476269620", "16445960190660", "17248202151180", "18852686072220", "608500527054420", "638183479593660", "697549384672140", "707176288198380", "772960128961020", "810665501105460", "26165522663340060", "28599524771557740", "29994623540902020", "33237285545323860", "1229779565176982820" ]
[ "nonn" ]
6
1
1
[ "A005101", "A005117", "A013929", "A048250", "A087248", "A357685", "A357686", "A357687" ]
null
Amiram Eldar, Oct 09 2022
2022-10-09T12:05:32
oeisdata/seq/A357/A357687.seq
41c4407cce35437eee97f4a7fdfa3773
A357688
Number of ways to write n as an ordered sum of four positive Fibonacci numbers (with a single type of 1).
[ "1", "4", "10", "16", "23", "28", "34", "36", "43", "48", "50", "48", "50", "56", "58", "64", "67", "60", "58", "52", "64", "64", "70", "68", "70", "76", "70", "72", "79", "60", "60", "48", "58", "68", "60", "84", "80", "64", "82", "64", "82", "88", "66", "76", "66", "64", "84", "60", "79", "60", "24", "60", "36", "60", "74", "48", "88", "76", "72", "96", "68", "88", "76", "48", "82", "60", "70" ]
[ "nonn" ]
42
4
2
[ "A000045", "A076739", "A121548", "A121549", "A121550", "A319397", "A357688", "A357690", "A357691" ]
null
Ilya Gutkovskiy, Oct 10 2022
2023-08-06T14:49:25
oeisdata/seq/A357/A357688.seq
0df823eac77993125d77eaa45d54d662
A357689
a(n) = n/A204455(n), where A204455(n) is the product of odd noncomposite divisors of n.
[ "1", "2", "1", "4", "1", "2", "1", "8", "3", "2", "1", "4", "1", "2", "1", "16", "1", "6", "1", "4", "1", "2", "1", "8", "5", "2", "9", "4", "1", "2", "1", "32", "1", "2", "1", "12", "1", "2", "1", "8", "1", "2", "1", "4", "3", "2", "1", "16", "7", "10", "1", "4", "1", "18", "1", "8", "1", "2", "1", "4", "1", "2", "3", "64", "1", "2", "1", "4", "1", "2", "1", "24", "1", "2", "5", "4", "1", "2", "1", "16", "27", "2", "1", "4", "1", "2", "1", "8", "1", "6", "1", "4", "1", "2", "1", "32", "1", "14", "3", "20" ]
[ "nonn", "mult", "easy" ]
30
1
2
[ "A000265", "A003557", "A006519", "A204455", "A324873", "A357689" ]
null
Juri-Stepan Gerasimov, Oct 09 2022
2022-10-18T03:40:14
oeisdata/seq/A357/A357689.seq
e75fc2fa390bdf08a0e0f0144e28cca3
A357690
Number of ways to write n as an ordered sum of five positive Fibonacci numbers (with a single type of 1).
[ "1", "5", "15", "30", "50", "71", "95", "115", "140", "165", "191", "205", "220", "240", "260", "285", "310", "325", "325", "320", "341", "350", "380", "385", "405", "420", "430", "450", "465", "465", "445", "410", "435", "425", "450", "481", "495", "515", "490", "510", "555", "525", "580", "540", "530", "570", "530", "580", "600", "520", "525", "440", "455", "520", "445", "555", "530" ]
[ "nonn" ]
16
5
2
[ "A000045", "A076739", "A121548", "A121549", "A121550", "A319398", "A357688", "A357690", "A357691" ]
null
Ilya Gutkovskiy, Oct 10 2022
2022-10-10T12:43:09
oeisdata/seq/A357/A357690.seq
893c035e22abf1d4c63cc489a4a7739e
A357691
Number of ways to write n as an ordered sum of six positive Fibonacci numbers (with a single type of 1).
[ "1", "6", "21", "50", "96", "156", "231", "312", "405", "506", "621", "726", "828", "930", "1041", "1160", "1290", "1422", "1520", "1590", "1677", "1766", "1887", "1980", "2106", "2196", "2310", "2426", "2550", "2670", "2706", "2700", "2736", "2756", "2850", "2916", "3071", "3156", "3186", "3296", "3396", "3510", "3621", "3636", "3765", "3720", "3840", "3966", "4010" ]
[ "nonn" ]
19
6
2
[ "A000045", "A076739", "A121548", "A121549", "A121550", "A319399", "A357688", "A357690", "A357691" ]
null
Ilya Gutkovskiy, Oct 10 2022
2022-10-10T12:49:52
oeisdata/seq/A357/A357691.seq
ff0c7cb8775bd84a906fe5ff026afaa6
A357692
Integers k such that A037278(k) is a term of A175252.
[ "1", "2", "4", "15", "16", "25", "60", "90", "100", "124", "150", "240", "375", "384", "600", "618", "625", "960", "1536", "3330", "3750", "4650", "5760", "10000", "10500", "10752", "15000", "16384", "17500", "24576", "25600", "40000", "49500", "62500", "102400", "139200", "168750", "198400", "323280", "526848", "960000", "1179648", "1248000", "1369125" ]
[ "nonn", "base" ]
26
1
2
[ "A037278", "A069872", "A175252", "A357692" ]
null
Michel Marcus, Oct 10 2022
2022-10-13T16:32:10
oeisdata/seq/A357/A357692.seq
0c3ba442beb3cbf5aebe3df800b1d41a
A357693
Expansion of e.g.f. cos( sqrt(2) * log(1+x) ).
[ "1", "0", "-2", "6", "-18", "60", "-216", "756", "-1620", "-14256", "349272", "-5452920", "78885576", "-1143659088", "17074183104", "-265437239760", "4316991698448", "-73572489226368", "1314108286270560", "-24584195654596512", "481215937895868384", "-9843358555320333120", "210128893733994567552" ]
[ "sign" ]
40
0
3
[ "A003703", "A357693", "A357718", "A357719", "A357720", "A357725" ]
null
Seiichi Manyama, Oct 10 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357693.seq
89597cceb45797a42e05ab10d872e681
A357694
Number of ways to write n as an ordered sum of seven positive Fibonacci numbers (with a single type of 1).
[ "1", "7", "28", "77", "168", "308", "504", "750", "1050", "1400", "1813", "2261", "2737", "3227", "3753", "4312", "4921", "5579", "6230", "6832", "7413", "8008", "8652", "9289", "9996", "10654", "11361", "12061", "12853", "13657", "14357", "14924", "15393", "15869", "16408", "16933", "17689", "18319", "18949", "19537", "20244", "21049", "21728" ]
[ "nonn" ]
24
7
2
[ "A000045", "A076739", "A121548", "A121549", "A121550", "A319400", "A357688", "A357690", "A357691", "A357694", "A357716", "A357717" ]
null
Ilya Gutkovskiy, Oct 10 2022
2022-10-10T16:11:04
oeisdata/seq/A357/A357694.seq
fee41b957ade63a2e705c1ed71f06d48
A357695
Cubefree abundant numbers.
[ "12", "18", "20", "30", "36", "42", "60", "66", "70", "78", "84", "90", "100", "102", "114", "126", "132", "138", "140", "150", "156", "174", "180", "186", "196", "198", "204", "210", "220", "222", "228", "234", "246", "252", "258", "260", "276", "282", "294", "300", "306", "308", "318", "330", "340", "342", "348", "350", "354", "364", "366", "372", "380", "390", "396" ]
[ "nonn" ]
11
1
1
[ "A000203", "A002117", "A004709", "A005101", "A087248", "A308618", "A357695", "A357696", "A357697" ]
null
Amiram Eldar, Oct 10 2022
2022-10-12T04:35:02
oeisdata/seq/A357/A357695.seq
f812e66444886ff87840ab271ebfefb7
A357696
Cubefree primitive abundant numbers: cubefree abundant numbers having no abundant proper divisor.
[ "12", "18", "20", "30", "42", "66", "70", "78", "102", "114", "138", "174", "186", "196", "222", "246", "258", "282", "308", "318", "354", "364", "366", "402", "426", "438", "474", "476", "498", "532", "534", "550", "572", "582", "606", "618", "642", "644", "650", "654", "678", "748", "762", "786", "812", "822", "834", "836", "868", "894", "906", "942", "978", "1002" ]
[ "nonn" ]
9
1
1
[ "A004709", "A091191", "A249242", "A308618", "A357695", "A357696" ]
null
Amiram Eldar, Oct 10 2022
2022-10-12T04:12:18
oeisdata/seq/A357/A357696.seq
fe83d4add758640262a29c0e40d3357e
A357697
Odd cubefree abundant numbers.
[ "1575", "2205", "3465", "4095", "5355", "5775", "5985", "6435", "6825", "7245", "8085", "8415", "8925", "9135", "9555", "9765", "11025", "11655", "12705", "12915", "13545", "14805", "15015", "16695", "17325", "18585", "19215", "19635", "20475", "21105", "21945", "22365", "22995", "23205", "24255", "24885", "25935", "26145", "26565", "26775" ]
[ "nonn" ]
12
1
1
[ "A000203", "A004709", "A005231", "A005408", "A112643", "A333950", "A357695", "A357697" ]
null
Amiram Eldar, Oct 10 2022
2022-10-12T04:33:41
oeisdata/seq/A357/A357697.seq
831f0f95c23ba2069602d8df6f386195
A357698
a(n) is the sum of the aliquot divisors of n that are cubefree.
[ "0", "1", "1", "3", "1", "6", "1", "7", "4", "8", "1", "16", "1", "10", "9", "7", "1", "21", "1", "22", "11", "14", "1", "28", "6", "16", "13", "28", "1", "42", "1", "7", "15", "20", "13", "55", "1", "22", "17", "42", "1", "54", "1", "40", "33", "26", "1", "28", "8", "43", "21", "46", "1", "39", "17", "56", "23", "32", "1", "108", "1", "34", "41", "7", "19", "78", "1", "58", "27", "74", "1", "91", "1", "40" ]
[ "nonn" ]
10
1
4
[ "A002117", "A004709", "A013661", "A073185", "A212793", "A293228", "A357698" ]
null
Amiram Eldar, Oct 10 2022
2022-10-12T04:36:13
oeisdata/seq/A357/A357698.seq
5a25dd72ed6ea6c83bff50451bc96f4a
A357699
Noncubefree numbers k such that A357698(k) > k.
[ "24", "40", "72", "120", "168", "200", "264", "280", "312", "360", "392", "408", "440", "456", "504", "520", "540", "552", "600", "616", "680", "696", "728", "744", "760", "792", "840", "888", "920", "936", "952", "984", "1032", "1064", "1128", "1144", "1160", "1176", "1224", "1240", "1272", "1288", "1320", "1368", "1400", "1416", "1464", "1480", "1496", "1560" ]
[ "nonn" ]
13
1
1
[ "A046099", "A357695", "A357698", "A357699" ]
null
Amiram Eldar, Oct 10 2022
2022-10-12T04:35:45
oeisdata/seq/A357/A357699.seq
a9a5e7d88fe00607a05959e355f35c6a
A357700
Noncubefree numbers k such that A073185(k) > 2*k.
[ "360360", "471240", "1801800", "2356200", "2522520", "2633400", "2784600", "3112200", "3187800", "3298680", "3686760", "3767400", "3898440", "3963960", "4019400", "4296600", "4462920", "4684680", "5128200", "5183640", "5682600", "5793480", "6126120", "6846840", "8011080", "8288280", "8953560", "10210200", "10450440" ]
[ "nonn" ]
9
1
1
[ "A073185", "A357695", "A357700" ]
null
Amiram Eldar, Oct 10 2022
2022-10-12T04:13:46
oeisdata/seq/A357/A357700.seq
a215577161195d4fd8ca2c634fc40aee