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7
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348
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score
int64
1
2.35k
offset_a
int64
-14,827
666,262,453B
offset_b
int64
0
635M
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1999-12-11 03:00:00
2025-07-19 00:40:46
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A364201
Lexicographically earliest sequence of distinct positive integers such that the sum of all terms a(1)..a(n) in binary is a substring of the concatenation of all terms a(1)..a(n) in binary.
[ "1", "2", "3", "5", "11", "7", "16", "9", "6", "18", "4", "13", "10", "15", "12", "23", "20", "8", "27", "19", "36", "26", "22", "17", "21", "31", "25", "14", "29", "28", "30", "57", "24", "32", "39", "43", "40", "34", "38", "46", "33", "35", "42", "37", "55", "44", "58", "48", "56", "52", "41", "45", "64", "63", "54", "61", "60", "49", "50", "51", "65", "47", "67", "88", "132", "73", "76", "68", "109", "59", "82", "87", "62", "98", "69", "70" ]
[ "nonn", "base" ]
13
1
2
[ "A007088", "A300000", "A339144", "A357082", "A359482", "A363186", "A364201" ]
null
Scott R. Shannon, Jul 13 2023
2023-08-09T16:57:44
oeisdata/seq/A364/A364201.seq
acf3711d17a1ee78397936d9cd7cc506
A364202
Integers m which can be written as m = p*q = r*s, with 1 <= r < p < q < s <= m and satisfying (p+q) | (s-r).
[ "6", "21", "24", "30", "40", "52", "54", "60", "72", "84", "96", "105", "120", "126", "150", "154", "160", "165", "180", "186", "189", "204", "208", "210", "216", "240", "270", "273", "288", "294", "300", "301", "312", "322", "330", "336", "342", "357", "360", "378", "384", "414", "420", "456", "468", "480", "486", "504", "525", "540", "546", "550", "594", "600" ]
[ "nonn" ]
107
1
1
[ "A003273", "A364202" ]
null
Jose Aranda, Jul 13 2023
2023-07-23T06:04:37
oeisdata/seq/A364/A364202.seq
7c0015e28e1b84ca476b3ab68a8b86f7
A364203
Triangle read by rows: T(n, k) is the number of n X n matrices of rank k using all the integers from 1 to n^2.
[ "1", "0", "24", "0", "2736", "360144" ]
[ "nonn", "hard", "more", "tabl" ]
14
1
3
[ "A085000", "A088020", "A350565", "A350566", "A364203", "A364206", "A364226" ]
null
Stefano Spezia, Jul 13 2023
2025-05-07T12:20:01
oeisdata/seq/A364/A364203.seq
49d7ffc3b4e412d791f22e2fea150bcd
A364204
Expansion of Sum_{k>=0} x^(3*k+1) / (1 + x^(3*k+1)).
[ "1", "-1", "1", "0", "1", "-1", "2", "-2", "1", "0", "1", "0", "2", "-2", "1", "-1", "1", "-1", "2", "-1", "2", "0", "1", "-2", "2", "-2", "1", "0", "1", "0", "2", "-3", "1", "0", "2", "0", "2", "-2", "2", "-2", "1", "-2", "2", "-1", "1", "0", "1", "-1", "3", "-1", "1", "0", "1", "-1", "2", "-4", "2", "0", "1", "-1", "2", "-2", "2", "-2", "2", "0", "2", "-1", "1", "0", "1", "-2", "2", "-2", "2", "0", "2", "-2", "2", "-3", "1", "0", "1", "0", "2", "-2", "1", "-2", "1", "0", "4", "-1" ]
[ "sign" ]
14
1
7
[ "A001817", "A048272", "A364011", "A364204", "A364205", "A364232" ]
null
Ilya Gutkovskiy, Jul 14 2023
2023-07-29T10:33:50
oeisdata/seq/A364/A364204.seq
ccf7313a3bb2e30439ccca788813d3a7
A364205
Expansion of Sum_{k>=0} x^(3*k+2) / (1 + x^(3*k+2)).
[ "0", "1", "0", "-1", "1", "1", "0", "0", "0", "0", "1", "-1", "0", "2", "1", "-2", "1", "1", "0", "-1", "0", "0", "1", "0", "1", "2", "0", "-2", "1", "0", "0", "-1", "1", "0", "2", "-1", "0", "2", "0", "-2", "1", "2", "0", "-1", "1", "0", "1", "-2", "0", "1", "1", "-2", "1", "1", "2", "0", "0", "0", "1", "-1", "0", "2", "0", "-3", "2", "0", "0", "-1", "1", "0", "1", "0", "0", "2", "1", "-2", "2", "2", "0", "-3", "0", "0", "1", "-2", "2", "2", "1", "-2", "1", "0", "0", "-1" ]
[ "sign" ]
13
1
14
[ "A001822", "A048272", "A364014", "A364204", "A364205", "A364235" ]
null
Ilya Gutkovskiy, Jul 14 2023
2023-07-29T10:34:52
oeisdata/seq/A364/A364205.seq
8dbb6a324ba2d7f1bccd6436ed46cca4
A364206
a(n) is the number of n X n nonsingular matrices using all the integers from 1 to n^2.
[ "1", "24", "360144", "20914499571840" ]
[ "nonn", "hard", "more" ]
16
1
2
[ "A085000", "A088020", "A136609", "A221976", "A350565", "A350566", "A364203", "A364206", "A364227" ]
null
Stefano Spezia, Jul 13 2023
2023-07-24T15:09:34
oeisdata/seq/A364/A364206.seq
27972e989ac0567c91a72651daae8f6b
A364207
Number of partitions of [n] such that the minimal element of each block is also its size.
[ "1", "1", "0", "1", "0", "0", "3", "1", "0", "0", "60", "45", "53", "24", "7", "12601", "15120", "33390", "55710", "66522", "86037", "37907754", "63130067", "202203684", "511378789", "1421634137", "2566309603", "5855352202", "2064277450957", "4418631559288", "18485494082571", "61020702809287", "232959438927000", "783244248553960" ]
[ "nonn" ]
28
0
7
[ "A000110", "A007837", "A188431", "A326493", "A327711", "A364207", "A364406" ]
null
Alois P. Heinz, Jul 13 2023
2023-10-21T01:44:49
oeisdata/seq/A364/A364207.seq
7623c28a73011426c5bbc2e27da202aa
A364208
a(n) is the number of full graphs on n unlabeled vertices (see comments for definition of full graph).
[ "1", "1", "2", "3", "10", "32", "154", "1037", "12339", "274640" ]
[ "nonn", "more" ]
42
1
3
null
null
Houston Schuerger, Aug 26 2023
2023-10-08T09:17:49
oeisdata/seq/A364/A364208.seq
a58f442198d41f7c3225cfecbe1e7309
A364209
Number of divisors of n of the form 3*k+1 that are at most sqrt(n).
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "2", "1", "1", "2", "1", "1", "1", "3", "1", "1", "1", "2", "1", "1", "2", "2", "1", "1", "1", "2", "1", "2", "1", "2", "1", "1", "1", "2", "2", "1", "1", "2", "1", "1", "1", "3", "1", "1", "1", "2", "1", "1", "2", "2", "1", "1", "1", "2", "1", "2", "1", "3" ]
[ "nonn" ]
28
1
16
[ "A001817", "A038548", "A364209", "A364357" ]
null
Ilya Gutkovskiy, Jul 21 2023
2023-07-23T13:03:54
oeisdata/seq/A364/A364209.seq
4efa72755b3ef0b358b8d1b73f44b81e
A364210
a(n) = (1/(2*n)) * Sum_{d|n} 3^(n/d-1) * phi(3*d).
[ "1", "2", "4", "8", "17", "44", "105", "278", "733", "1978", "5369", "14792", "40881", "113934", "318884", "896948", "2532161", "7174862", "20390553", "58114072", "166037460", "475473286", "1364393897", "3922640132", "11297181473", "32588043882", "94143179560", "272342824320", "788854912241", "2287679406940", "6641649422409" ]
[ "nonn" ]
9
1
2
[ "A000010", "A000013", "A034754", "A195459", "A327625", "A364210", "A364211", "A364212" ]
null
Seiichi Manyama, Jul 13 2023
2023-07-14T09:03:16
oeisdata/seq/A364/A364210.seq
9bd4fc3dd5c56440a1ea0fcb56b3cc41
A364211
a(n) = (1/(4*n)) * Sum_{d|n} 5^(n/d-1) * phi(5*d).
[ "1", "3", "9", "33", "126", "527", "2233", "9783", "43409", "195378", "887785", "4069297", "18780049", "87194199", "406901134", "1907353533", "8975758273", "42385547227", "200773540297", "953674414158", "4541306270097", "21674416725855", "103660251783289", "496705375169547", "2384185791015751", "11462431696965147", "55189485903168409" ]
[ "nonn" ]
9
1
2
[ "A000010", "A000013", "A343492", "A359100", "A359101", "A364210", "A364211", "A364212" ]
null
Seiichi Manyama, Jul 13 2023
2023-07-14T08:47:52
oeisdata/seq/A364/A364211.seq
6338acd5c97ac3c42d0c33caf72cfeee
A364212
a(n) = (1/(6*n)) * Sum_{d|n} 7^(n/d-1) * phi(7*d).
[ "1", "4", "17", "88", "481", "2812", "16808", "102988", "640545", "4035604", "25679569", "164778696", "1064714401", "6920652008", "45214871857", "296722645888", "1954878268801", "12923917765876", "85705978837393", "569944761286648", "3799631728468936", "25388448380261788", "169992219503608177", "1140364472585830196" ]
[ "nonn" ]
8
1
2
[ "A000010", "A000013", "A359099", "A359102", "A364210", "A364211", "A364212" ]
null
Seiichi Manyama, Jul 13 2023
2023-07-14T09:04:02
oeisdata/seq/A364/A364212.seq
52e0d8217856358d3f77fd6b0a00396c
A364213
The number of trailing 0's in the canonical representation of n as a sum of distinct Jacobsthal numbers (A280049).
[ "0", "0", "2", "0", "0", "0", "0", "2", "0", "0", "4", "0", "0", "2", "0", "0", "0", "0", "2", "0", "0", "0", "0", "2", "0", "0", "0", "0", "2", "0", "0", "4", "0", "0", "2", "0", "0", "0", "0", "2", "0", "0", "6", "0", "0", "2", "0", "0", "0", "0", "2", "0", "0", "4", "0", "0", "2", "0", "0", "0", "0", "2", "0", "0", "0", "0", "2", "0", "0", "0", "0", "2", "0", "0", "4", "0", "0", "2", "0", "0", "0", "0", "2", "0", "0", "0", "0" ]
[ "nonn", "base", "easy" ]
9
1
3
[ "A007583", "A007814", "A122840", "A280049", "A364213" ]
null
Amiram Eldar, Jul 14 2023
2023-07-15T05:52:30
oeisdata/seq/A364/A364213.seq
85464697969e654577b9a27b920b8210
A364214
Numbers whose canonical representation as a sum of distinct Jacobsthal numbers (A280049) is palindromic.
[ "1", "2", "4", "5", "6", "10", "12", "15", "18", "21", "22", "30", "34", "42", "44", "49", "58", "63", "66", "71", "80", "85", "86", "102", "110", "126", "130", "146", "154", "170", "172", "183", "198", "209", "218", "229", "244", "255", "258", "269", "284", "295", "304", "315", "330", "341", "342", "374", "390", "422", "430", "462", "478", "510", "514", "546", "562", "594" ]
[ "nonn", "base", "easy" ]
9
1
2
[ "A001045", "A002113", "A002450", "A003159", "A006995", "A014190", "A020988", "A094202", "A280049", "A331191", "A351712", "A351717", "A352087", "A352105", "A352319", "A352341", "A364214" ]
null
Amiram Eldar, Jul 14 2023
2024-03-30T23:07:46
oeisdata/seq/A364/A364214.seq
62fb60ff6c27544ff39e4ee3e073bd63
A364215
The number of 1's in the canonical representation of n as a sum of distinct Jacobsthal numbers (A280049).
[ "1", "2", "1", "2", "3", "2", "3", "2", "3", "4", "1", "2", "3", "2", "3", "4", "3", "4", "3", "4", "5", "2", "3", "2", "3", "4", "3", "4", "3", "4", "5", "2", "3", "4", "3", "4", "5", "4", "5", "4", "5", "6", "1", "2", "3", "2", "3", "4", "3", "4", "3", "4", "5", "2", "3", "4", "3", "4", "5", "4", "5", "4", "5", "6", "3", "4", "3", "4", "5", "4", "5", "4", "5", "6", "3", "4", "5", "4", "5", "6", "5", "6", "5", "6", "7", "2", "3" ]
[ "nonn", "base", "easy" ]
7
1
2
[ "A000120", "A003159", "A007583", "A007953", "A280049", "A364215" ]
null
Amiram Eldar, Jul 14 2023
2023-07-15T05:52:53
oeisdata/seq/A364/A364215.seq
5eaeab1e880a56725e5d3e943225ff52
A364216
Jacobsthal-Niven numbers: numbers that are divisible by the sum of the digits in their Jacobsthal representation (A280049).
[ "1", "2", "3", "4", "6", "8", "9", "11", "12", "14", "15", "16", "20", "22", "24", "27", "28", "32", "33", "36", "40", "42", "43", "44", "45", "46", "48", "51", "52", "54", "56", "57", "60", "68", "72", "75", "76", "84", "86", "87", "88", "92", "93", "95", "96", "99", "100", "104", "105", "108", "112", "115", "117", "120", "125", "126", "128", "129", "132", "135", "136", "138", "140" ]
[ "nonn", "base", "easy" ]
6
1
2
[ "A005349", "A007583", "A049445", "A064150", "A064438", "A064481", "A118363", "A280049", "A328208", "A328212", "A331085", "A331728", "A333426", "A334308", "A342426", "A342726", "A344341", "A351714", "A351719", "A352089", "A352107", "A352320", "A352342", "A352508", "A364215", "A364216", "A364217", "A364218", "A364219", "A364220", "A364221" ]
null
Amiram Eldar, Jul 14 2023
2023-07-15T05:53:05
oeisdata/seq/A364/A364216.seq
6de1b83925317b412766c02a67b8ca13
A364217
Numbers k such that k and k+1 are both Jacobsthal-Niven numbers (A364216).
[ "1", "2", "3", "8", "11", "14", "15", "27", "32", "42", "43", "44", "45", "51", "56", "75", "86", "87", "92", "95", "99", "104", "125", "128", "135", "144", "155", "171", "176", "182", "183", "195", "204", "264", "267", "275", "287", "305", "344", "363", "375", "387", "428", "444", "455", "474", "497", "512", "524", "535", "544", "545", "552", "555", "581", "605", "623", "639" ]
[ "nonn", "base", "easy" ]
8
1
2
[ "A328205", "A328209", "A328213", "A330927", "A330931", "A331086", "A331820", "A333427", "A334309", "A342427", "A344342", "A351715", "A351720", "A352090", "A352108", "A352321", "A352343", "A352509", "A364215", "A364216", "A364217", "A364218", "A364219", "A364220", "A364221" ]
null
Amiram Eldar, Jul 14 2023
2023-07-15T05:53:16
oeisdata/seq/A364/A364217.seq
ea4cab0eed78870b77360215f6438db6
A364218
Starts of runs of 3 consecutive integers that are Jacobsthal-Niven numbers (A364216).
[ "1", "2", "14", "42", "43", "44", "86", "182", "544", "686", "846", "854", "1014", "1375", "1384", "1504", "1624", "2105", "2190", "2315", "2358", "2731", "2732", "2763", "2774", "2824", "3243", "3534", "3702", "4205", "4878", "5046", "5408", "5462", "5643", "5663", "6222", "6390", "6935", "7566", "7734", "7928", "8224", "8704", "8910", "9078", "9368" ]
[ "nonn", "base", "easy" ]
6
1
2
[ "A154701", "A328206", "A328210", "A328214", "A330932", "A331087", "A331822", "A333428", "A334310", "A342428", "A344343", "A351716", "A351721", "A352091", "A352109", "A352322", "A352344", "A352510", "A364216", "A364217", "A364218", "A364219", "A364220", "A364221" ]
null
Amiram Eldar, Jul 14 2023
2023-07-15T05:53:28
oeisdata/seq/A364/A364218.seq
625c2e25faf1b550c332798fd661ee7e
A364219
Starts of runs of 4 consecutive integers that are Jacobsthal-Niven numbers (A364216).
[ "1", "42", "43", "2731", "11605", "13024", "14229", "25983", "39390", "45727", "46624", "47529", "60073", "96039", "111390", "131103", "132010", "133984", "134430", "140767", "148180", "148181", "148509", "174762", "174763", "187744", "197790", "237609", "247114", "266453", "275229", "287988", "312190", "330847", "354429", "370269" ]
[ "nonn", "base" ]
6
1
2
[ "A141769", "A328207", "A328211", "A328215", "A330933", "A331824", "A334311", "A342429", "A344344", "A352092", "A352110", "A352345", "A352511", "A364216", "A364217", "A364218", "A364219", "A364220", "A364221" ]
null
Amiram Eldar, Jul 14 2023
2023-07-15T05:53:37
oeisdata/seq/A364/A364219.seq
177f5b8b6963d752efed44ff0d83d83a
A364220
Starts of runs of 5 consecutive integers that are Jacobsthal-Niven numbers (A364216).
[ "42", "148180", "174762", "2366376", "2809300", "3758676", "3938856", "4463016", "4987176", "6559656", "6817149", "11975380", "12325416", "12849576", "13029756", "13373736", "15470376", "17567016", "18271356", "23332776", "23512956", "24037116", "24561276", "25953576", "26657916", "27974439", "28754556", "28754557" ]
[ "nonn", "base" ]
6
1
1
[ "A330928", "A364216", "A364217", "A364218", "A364219", "A364220", "A364221" ]
null
Amiram Eldar, Jul 14 2023
2023-07-15T05:53:45
oeisdata/seq/A364/A364220.seq
6d1be3e36b0233c167671a1f3ef8dd18
A364221
Starts of runs of 6 consecutive integers that are Jacobsthal-Niven numbers (A364216).
[ "28754556", "103529256", "121576571", "288033576", "293979516", "414100179", "497440040", "584411859", "766411476", "858663636", "1498843176", "1591095336", "1637221416", "1683347496", "1775599656", "1816140156", "2341109715", "2789551400", "2882625576", "3042399699", "3044066856", "3067129896", "3240102696" ]
[ "nonn", "base" ]
6
1
1
[ "A330929", "A364216", "A364217", "A364218", "A364219", "A364220", "A364221" ]
null
Amiram Eldar, Jul 14 2023
2023-07-15T05:53:53
oeisdata/seq/A364/A364221.seq
68a18a5e01673d380f3e44f5816a8b07
A364222
Expansion of Sum_{k>=0} 3^k * x^(3^k) / (1 - x^(3^k))^2.
[ "1", "2", "6", "4", "5", "12", "7", "8", "27", "10", "11", "24", "13", "14", "30", "16", "17", "54", "19", "20", "42", "22", "23", "48", "25", "26", "108", "28", "29", "60", "31", "32", "66", "34", "35", "108", "37", "38", "78", "40", "41", "84", "43", "44", "135", "46", "47", "96", "49", "50", "102", "52", "53", "216", "55", "56", "114", "58", "59", "120", "61", "62", "189", "64", "65", "132", "67", "68", "138", "70", "71", "216", "73", "74" ]
[ "nonn", "mult", "easy" ]
17
1
2
[ "A007949", "A051064", "A091512", "A327625", "A364222", "A364223", "A364224" ]
null
Seiichi Manyama, Jul 14 2023
2023-07-14T12:12:41
oeisdata/seq/A364/A364222.seq
429720fe8865c23f19c54ee9ead56d07
A364223
Expansion of Sum_{k>=0} 5^k * x^(5^k) / (1 - x^(5^k))^2.
[ "1", "2", "3", "4", "10", "6", "7", "8", "9", "20", "11", "12", "13", "14", "30", "16", "17", "18", "19", "40", "21", "22", "23", "24", "75", "26", "27", "28", "29", "60", "31", "32", "33", "34", "70", "36", "37", "38", "39", "80", "41", "42", "43", "44", "90", "46", "47", "48", "49", "150", "51", "52", "53", "54", "110", "56", "57", "58", "59", "120", "61", "62", "63", "64", "130", "66", "67", "68", "69", "140", "71", "72", "73", "74", "225" ]
[ "nonn", "easy", "mult" ]
15
1
2
[ "A055457", "A091512", "A112765", "A359100", "A364222", "A364223", "A364224" ]
null
Seiichi Manyama, Jul 14 2023
2023-07-15T05:54:06
oeisdata/seq/A364/A364223.seq
f2b43e9deb2e5cc23752552d521c93dd
A364224
Expansion of Sum_{k>=0} 7^k * x^(7^k) / (1 - x^(7^k))^2.
[ "1", "2", "3", "4", "5", "6", "14", "8", "9", "10", "11", "12", "13", "28", "15", "16", "17", "18", "19", "20", "42", "22", "23", "24", "25", "26", "27", "56", "29", "30", "31", "32", "33", "34", "70", "36", "37", "38", "39", "40", "41", "84", "43", "44", "45", "46", "47", "48", "147", "50", "51", "52", "53", "54", "55", "112", "57", "58", "59", "60", "61", "62", "126", "64", "65", "66", "67", "68", "69", "140", "71", "72", "73", "74", "75", "76", "154" ]
[ "nonn", "easy", "mult" ]
17
1
2
[ "A091512", "A214411", "A359099", "A364222", "A364223", "A364224" ]
null
Seiichi Manyama, Jul 14 2023
2023-07-14T15:36:30
oeisdata/seq/A364/A364224.seq
797c43ad1b3c540798ef5fcf5917c65d
A364225
a(n) = number of k <= m such that rad(k) | m, where m = A025487(n) and rad(n) = A007947(n).
[ "1", "2", "3", "5", "4", "8", "5", "11", "18", "6", "14", "15", "26", "7", "18", "20", "36", "8", "23", "44", "25", "68", "26", "49", "9", "29", "58", "31", "96", "32", "65", "10", "35", "76", "38", "131", "39", "83", "84", "11", "88", "42", "156", "43", "97", "45", "174", "46", "104", "106", "12", "111", "50", "283", "206", "51", "121", "53", "228", "54", "130", "133", "13", "138", "58" ]
[ "nonn" ]
70
1
2
[ "A001221", "A002110", "A007947", "A010846", "A025487", "A363061", "A364225" ]
null
Michael De Vlieger, Oct 24 2023
2023-11-19T10:33:30
oeisdata/seq/A364/A364225.seq
ddc84b1b4ca39b6e604b37051ddf5f83
A364226
Triangle read by rows: T(n, k) is the number of n X n matrices of rank k using all the first n^2 prime numbers.
[ "1", "0", "24", "0", "216", "362664" ]
[ "nonn", "hard", "more", "tabl" ]
9
1
3
[ "A088020", "A180128", "A350858", "A350859", "A364203", "A364226", "A364227" ]
null
Stefano Spezia, Jul 15 2023
2023-08-02T14:41:30
oeisdata/seq/A364/A364226.seq
379085901183729449e929c3a31a1e6a
A364227
a(n) is the number of n X n nonsingular matrices using all the first n^2 prime numbers.
[ "1", "24", "362664" ]
[ "nonn", "bref", "hard", "more" ]
7
1
2
[ "A180128", "A350858", "A350859", "A364206", "A364226", "A364227" ]
null
Stefano Spezia, Jul 15 2023
2023-08-02T14:41:44
oeisdata/seq/A364/A364227.seq
89b478ab6551961c43d2c861825011d9
A364228
Triangle read by rows: T(n, k) is the number of n X n Hermitian Toeplitz matrices of rank k using all the integers 1, 2, ..., n and with all off-diagonal elements purely imaginary.
[ "1", "0", "2", "0", "1", "5", "0", "0", "0", "24", "0", "0", "0", "0", "120", "0", "0", "0", "0", "1", "719", "0", "0", "0", "0", "0", "0", "5040", "0", "0", "0", "0", "0", "2", "1", "40317", "0", "0", "0", "0", "0", "0", "0", "6", "362874", "0", "0", "0", "0", "0", "0", "1", "0", "1", "3628798" ]
[ "nonn", "more", "tabl" ]
10
1
3
[ "A000142", "A359614", "A359615", "A359616", "A359617", "A364228", "A364229" ]
null
Stefano Spezia, Jul 14 2023
2023-08-02T14:42:03
oeisdata/seq/A364/A364228.seq
1eb13e7f8a7fff786405630f79e18bcc
A364229
a(n) is the number of n X n nonsingular Hermitian Toeplitz matrices using all the integers 1, 2, ..., n and with all off-diagonal elements purely imaginary.
[ "1", "2", "5", "24", "120", "719", "5040", "40317", "362874", "3628798" ]
[ "nonn", "hard", "more" ]
9
1
2
[ "A359614", "A359615", "A359616", "A359617", "A364228", "A364229" ]
null
Stefano Spezia, Jul 14 2023
2023-08-02T14:42:27
oeisdata/seq/A364/A364229.seq
22c98946efb761bf68cfe87f4d272d02
A364230
Triangle read by rows: T(n, k) is the number of n X n symmetric Toeplitz matrices of rank k using all the integers 1, 2, ..., n.
[ "1", "0", "2", "0", "0", "6", "0", "0", "0", "24", "0", "0", "0", "0", "120", "0", "0", "0", "0", "2", "718", "0", "0", "0", "0", "4", "31", "5005", "0", "0", "0", "0", "0", "2", "44", "40274", "0", "0", "0", "0", "0", "0", "4", "272", "362604", "0", "0", "0", "0", "0", "0", "0", "111", "774", "3627915", "0", "0", "0", "0", "0", "0", "2", "14", "244", "6974", "39909566", "0", "0", "0", "0", "0", "0", "0", "4", "64", "743", "9533", "478991256" ]
[ "nonn", "tabl" ]
17
1
3
[ "A000142", "A350953", "A350954", "A351019", "A351020", "A356865", "A364230", "A364231" ]
null
Stefano Spezia, Jul 14 2023
2023-12-30T23:04:23
oeisdata/seq/A364/A364230.seq
db8709476a5aa122c4e5ace2fa775be5
A364231
a(n) is the number of n X n nonsingular symmetric Toeplitz matrices using all the integers 1, 2, ..., n.
[ "1", "2", "6", "24", "120", "718", "5005", "40274", "362604", "3627915", "39909566", "478991256" ]
[ "nonn", "hard", "more" ]
12
1
2
[ "A350953", "A350954", "A351019", "A351020", "A356865", "A364230", "A364231" ]
null
Stefano Spezia, Jul 14 2023
2023-12-30T23:04:38
oeisdata/seq/A364/A364231.seq
e0f036bab541434d12652d75f18bfd0d
A364232
Expansion of Sum_{k>=0} x^(3*k+1) / (1 + x^(3*k+1))^2.
[ "1", "-2", "3", "-3", "5", "-6", "8", "-10", "9", "-9", "11", "-9", "14", "-16", "15", "-19", "17", "-18", "20", "-17", "24", "-21", "23", "-30", "26", "-28", "27", "-24", "29", "-27", "32", "-42", "33", "-33", "40", "-27", "38", "-40", "42", "-53", "41", "-48", "44", "-35", "45", "-45", "47", "-57", "57", "-47", "51", "-42", "53", "-54", "56", "-80", "60", "-57", "59", "-51", "62", "-64", "72", "-83", "70", "-63", "68", "-53", "69", "-72" ]
[ "sign" ]
13
1
2
[ "A002129", "A186690", "A326399", "A364012", "A364204", "A364232", "A364235" ]
null
Ilya Gutkovskiy, Jul 14 2023
2023-07-29T10:37:14
oeisdata/seq/A364/A364232.seq
48587bbda18f59c59cd875e9d2e68c13
A364233
Triangle read by rows: T(n, k) is the number of n X n symmetric Toeplitz matrices of rank k using all the first n prime numbers integers.
[ "1", "0", "2", "0", "0", "6", "0", "0", "0", "24", "0", "0", "0", "0", "120", "0", "0", "0", "0", "2", "718", "0", "0", "0", "0", "0", "4", "5036", "0", "0", "0", "0", "0", "1", "3", "40316", "0", "0", "0", "0", "0", "0", "0", "18", "362862", "0", "0", "0", "0", "0", "0", "0", "0", "14", "3628786", "0", "0", "0", "0", "0", "0", "0", "0", "0", "99", "39916701", "0", "0", "0", "0", "0", "0", "0", "0", "0", "5", "78", "479001517" ]
[ "nonn", "tabl" ]
15
1
3
[ "A000142", "A348891", "A350955", "A350956", "A351021", "A351022", "A364233", "A364234" ]
null
Stefano Spezia, Jul 14 2023
2023-12-31T12:42:22
oeisdata/seq/A364/A364233.seq
6e40906d7cbdc7ff45b04293a3f4eb56
A364234
a(n) is the number of n X n nonsingular symmetric Toeplitz matrices using all the first n prime numbers.
[ "1", "2", "6", "24", "120", "718", "5036", "40316", "362862", "3628786", "39916701", "479001517" ]
[ "nonn", "hard", "more" ]
12
1
2
[ "A348891", "A350955", "A350956", "A351021", "A351022", "A364233", "A364234" ]
null
Stefano Spezia, Jul 14 2023
2023-12-31T12:43:11
oeisdata/seq/A364/A364234.seq
b5c929230cb779488e7008e97188f03a
A364235
Expansion of Sum_{k>=0} x^(3*k+2) / (1 + x^(3*k+2))^2.
[ "0", "1", "0", "-2", "1", "3", "0", "-3", "0", "3", "1", "-6", "0", "8", "3", "-10", "1", "9", "0", "-13", "0", "9", "1", "-9", "5", "14", "0", "-16", "1", "9", "0", "-19", "3", "15", "8", "-18", "0", "20", "0", "-25", "1", "24", "0", "-25", "9", "21", "1", "-30", "0", "16", "3", "-28", "1", "27", "16", "-24", "0", "27", "1", "-39", "0", "32", "0", "-42", "14", "27", "0", "-37", "3", "24", "1", "-27", "0", "38", "15", "-40", "8", "42", "0", "-69" ]
[ "sign" ]
13
1
4
[ "A002129", "A186690", "A326400", "A364015", "A364205", "A364232", "A364235" ]
null
Ilya Gutkovskiy, Jul 14 2023
2023-07-29T10:35:51
oeisdata/seq/A364/A364235.seq
e315fc2705e07cc9d4c92e7024c1f697
A364236
a(1) = 1. For n > 1, if a(n-1) is a novel term, a(n) = d(a(n-1)), else if a(n-1) is a repeat term seen k (>1) times, a(n) = a(n-1) + d(k-1), where d is the divisor counting function A000005.
[ "1", "1", "2", "2", "3", "2", "4", "3", "4", "5", "2", "4", "6", "4", "6", "7", "2", "5", "6", "8", "4", "7", "8", "9", "3", "5", "7", "9", "10", "4", "6", "8", "10", "11", "2", "4", "8", "10", "12", "6", "9", "11", "12", "13", "2", "6", "8", "11", "13", "14", "4", "6", "10", "12", "14", "15", "4", "8", "10", "13", "15", "16", "5", "7", "9", "11", "13", "15", "17", "2", "4", "7", "10", "12", "14", "16", "17", "18" ]
[ "nonn", "look" ]
22
1
3
[ "A000005", "A000027", "A345147", "A360179", "A364236" ]
null
David James Sycamore, Jul 14 2023
2023-07-15T08:49:11
oeisdata/seq/A364/A364236.seq
9d007c8daa965ca45f6c9b223fa56489
A364237
a(n) is the number of non-equivalent permutations of {1,2,...,2n-1} such that no subset of consecutive terms from the permutation sums to 0 modulo 2n, where two permutations are equivalent if one can be obtained from the other by multiplying every entry with an integer relatively prime to 2n and/or reversing the permutation.
[ "1", "1", "2", "4", "42", "504", "7492", "172480", "8639632" ]
[ "nonn", "hard", "more" ]
14
1
3
[ "A141599", "A364237" ]
null
Anna Coleman, Joshua Harrington, Maggie X. Lai, Philip Thomas, and Wing Hong Tony Wong, Jul 18 2023
2023-09-11T23:02:43
oeisdata/seq/A364/A364237.seq
98a22c35fbd066d10f1c287781163c56
A364238
Indices of records in A094605.
[ "1", "2", "4", "5", "7", "8", "10", "16", "17", "25", "26", "28", "30", "35", "37", "38", "40", "42", "44" ]
[ "nonn", "hard", "more" ]
16
1
2
[ "A070950", "A094605", "A363343", "A364238" ]
null
Paolo Xausa, Jul 15 2023
2025-02-16T08:34:06
oeisdata/seq/A364/A364238.seq
95c80b241bd24ab5d470aa2de556492d
A364239
Indices of records in A363345.
[ "1", "4", "9", "30", "401", "87868" ]
[ "nonn", "hard", "more" ]
15
1
2
[ "A070950", "A363344", "A363345", "A364239" ]
null
Paolo Xausa, Jul 15 2023
2025-02-16T08:34:06
oeisdata/seq/A364/A364239.seq
e0f7bf153c6435b6d7589ea471755dd4
A364240
a(n) is the periodic part (converted to base 10), on the n-th diagonal from the left of rule-30 1-D cellular automaton, when started from a single ON cell.
[ "1", "1", "0", "1", "1", "2", "2", "0", "12", "1", "6", "2", "13", "11", "6", "3", "11", "8", "6", "12", "6", "7", "3", "2", "8", "9", "14", "13", "0", "180", "1", "90", "74", "25", "156", "224", "98", "250", "123", "12", "20", "239", "215", "138", "20", "12", "159", "192", "58", "253", "139", "86", "195", "164", "25", "28", "48", "235", "159", "162", "213", "152", "25", "8", "14", "239" ]
[ "nonn", "base" ]
15
1
6
[ "A070950", "A363344", "A363345", "A363346", "A364240", "A364241" ]
null
Paolo Xausa, Jul 15 2023
2025-02-16T08:34:06
oeisdata/seq/A364/A364240.seq
1eccdd8e7ff88b28d7abff1a3fe77a01
A364241
a(n) is the initial transient (converted to base 10), before the periodic part, on the n-th diagonal from the left of rule-30 1-D cellular automaton, when started from a single ON cell, or -1 if there is no transient part.
[ "-1", "-1", "1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "1", "1", "-1", "4", "9", "0", "228", "63", "1241", "69", "7609", "2944", "11356", "255", "28487", "30890", "42037", "24160", "104333", "19167", "132196", "25361", "1042145", "473564", "4512243", "153187", "258856349", "2950249", "353554884", "104435283", "26762321451", "2005002052" ]
[ "sign", "base" ]
13
1
14
[ "A070950", "A363344", "A363345", "A363346", "A364240", "A364241" ]
null
Paolo Xausa, Jul 15 2023
2025-02-16T08:34:06
oeisdata/seq/A364/A364241.seq
87975afb76c8e1941b2b98b96755aa8e
A364242
a(n) is the smallest positive integer such that a(n) and a(n)+2 are both products of n distinct prime factors.
[ "3", "33", "663", "18445", "887313", "84946015", "3086525013", "557027507463", "31110090768183", "3404401335645583", "609352762511672905" ]
[ "nonn", "hard", "more" ]
18
1
1
[ "A005117", "A052215", "A364242" ]
null
Tomek Czajka, Jul 15 2023
2023-08-14T16:29:40
oeisdata/seq/A364/A364242.seq
92eda1a6cf58becae3d32ac86c031e70
A364243
a(n) = A108625(2*n-1, n-1) for n >= 1.
[ "1", "13", "271", "6637", "176251", "4914427", "141573251", "4174790893", "125288929171", "3811804637263", "117248436333601", "3638993432201563", "113790712076898871", "3580847269415337487", "113299135244467189771", "3601766951734150461677", "114973519461796962202051" ]
[ "nonn", "easy" ]
13
1
2
[ "A005258", "A108625", "A363867", "A364243", "A364244" ]
null
Peter Bala, Jul 16 2023
2023-07-18T04:09:55
oeisdata/seq/A364/A364243.seq
78856cba5c140bf9937e0dfeb83ed6d8
A364244
a(n) = A143007(2*n-1, n-1) for n >= 1.
[ "1", "25", "1441", "107353", "9073501", "826861993", "79219824685", "7865844936025", "802198564524325", "83532710607121525", "8844234718023010681", "949244022625120188265", "103044177225432902852641", "11293765432962617876667253", "1248038875078327818254657941" ]
[ "nonn", "easy" ]
21
1
2
[ "A005259", "A143007", "A363864", "A364243", "A364244" ]
null
Peter Bala, Jul 16 2023
2023-11-04T02:52:57
oeisdata/seq/A364/A364244.seq
bc2b6ab64799b4a7c99b0b79fc2ac759
A364245
Number of parts in all partitions of 2n into parts with multiplicity <= n.
[ "0", "1", "8", "24", "65", "150", "330", "657", "1274", "2338", "4172", "7203", "12171", "20045", "32474", "51623", "80867", "124841", "190406", "286857", "427758", "631367", "923544", "1339226", "1926798", "2751094", "3900931", "5494411", "7690923", "10701618", "14808183", "20380969", "27910066", "38035633", "51597166", "69685656" ]
[ "nonn" ]
8
0
3
[ "A210485", "A232623", "A364245" ]
null
Alois P. Heinz, Jul 15 2023
2023-07-16T15:31:08
oeisdata/seq/A364/A364245.seq
12a147f13d8d758a1f88336a450514a5
A364246
a(1) = 1. Thereafter, a(n) is the least novel multiple of either prime(k+1) if rad(a(n-1)) = A002110(k), or Product_{prime q; q < gpf(a(n-1)); and q!|a(n-1)} q otherwise.
[ "1", "2", "3", "4", "6", "5", "12", "10", "9", "8", "15", "14", "30", "7", "60", "21", "20", "18", "25", "24", "35", "36", "40", "27", "16", "33", "70", "39", "770", "42", "45", "22", "105", "26", "1155", "28", "75", "32", "48", "50", "51", "10010", "54", "55", "84", "65", "462", "80", "57", "170170", "63", "90", "49", "120", "56", "135", "34", "15015", "38", "255255", "44", "210" ]
[ "nonn" ]
24
1
2
[ "A002110", "A006530", "A007947", "A362889", "A364154", "A364246" ]
null
David James Sycamore, Jul 15 2023
2023-12-17T08:06:58
oeisdata/seq/A364/A364246.seq
675293a7b59251a09dd8db91c43005a4
A364247
Squares visited by the chess king on a spiral-numbered board, where the king moves to the square with the fewest steps to reach 1 using the 3x+1 function. In case of a tie, the king moves to the square with the smallest number.
[ "1", "2", "4", "16", "5", "6", "8", "24", "10", "26", "48", "80", "120", "168", "122", "170", "226", "227", "228", "172", "173", "174", "232", "176", "128", "88", "56", "90", "92", "136", "93", "58", "32", "13", "3", "12", "11", "28", "52", "84", "85", "53", "29", "30", "31", "57", "89", "130", "180", "181", "131", "132", "133", "184", "244", "186", "245", "312", "246", "314" ]
[ "nonn", "walk", "fini" ]
29
1
2
[ "A006577", "A014682", "A316667", "A326922", "A328928", "A328929", "A329520", "A330008", "A335816", "A364247" ]
null
Wagner Martins, Jul 15 2023
2023-08-07T09:55:27
oeisdata/seq/A364/A364247.seq
cb97a41533353b5330fb39472b7b4d34
A364248
For n >= 3, a(n) is the least r >= 0 such that the elliptic equation y^2 = n^3 + n^2 + 2*r*n + r^2 has an integer solution.
[ "0", "2", "5", "9", "14", "0", "27", "5", "44", "12", "65", "21", "0", "32", "119", "9", "152", "35", "21", "77", "230", "0", "275", "117", "54", "14", "377", "41", "434", "32", "55", "221", "0", "27", "629", "285", "52", "20", "779", "49", "860", "11", "21", "437", "1034", "0", "1127", "75", "34", "182", "1325", "27", "110", "159", "19", "725", "1652", "10", "1769", "837", "0", "320", "195", "99", "2144", "374" ]
[ "nonn" ]
62
3
2
[ "A000040", "A000096", "A000217", "A002061", "A005563", "A006254", "A054504", "A081119", "A364248", "A364421" ]
null
Ctibor O. Zizka, Sep 01 2023
2025-02-16T08:34:06
oeisdata/seq/A364/A364248.seq
d814c51641030b39aa722d69ad818190
A364249
Dirichlet inverse of A359374.
[ "1", "-1", "0", "1", "-1", "-1", "-1", "-1", "0", "1", "-1", "2", "-1", "1", "0", "1", "-1", "-1", "-1", "-1", "0", "1", "-1", "-3", "0", "1", "0", "-1", "-1", "1", "-1", "-1", "0", "1", "1", "3", "-1", "1", "0", "1", "-1", "1", "-1", "-1", "0", "1", "-1", "4", "0", "0", "0", "-1", "-1", "-1", "1", "1", "0", "1", "-1", "-2", "-1", "1", "0", "1", "1", "1", "-1", "-1", "0", "-1", "-1", "-6", "-1", "1", "0", "-1", "1", "1", "-1", "-1", "0", "1", "-1", "-2", "1", "1", "0", "1", "-1", "1", "1", "-1", "0", "1", "1", "-5" ]
[ "sign" ]
10
1
12
[ "A359374", "A364249", "A364250" ]
null
Antti Karttunen, Jul 17 2023
2023-07-17T17:12:57
oeisdata/seq/A364/A364249.seq
12ccb7c7cbb271a79986e300791f37dd
A364250
a(n) = A364249(n) mod 2.
[ "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "0", "0", "0", "0", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "0", "0", "0", "1", "1", "1", "1", "0" ]
[ "nonn" ]
10
1
null
[ "A000035", "A349348", "A359374", "A364249", "A364250" ]
null
Antti Karttunen, Jul 17 2023
2023-07-17T17:59:54
oeisdata/seq/A364/A364250.seq
0fd7b177744fde65606192e158256a47
A364251
a(n) = 1 if n is of the form q*(2^k), where q is one of the Mersenne primes (A000668) and k >= 0, otherwise a(n) = 0.
[ "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0" ]
[ "nonn" ]
12
1
null
[ "A000668", "A331410", "A335431", "A336923", "A364251", "A364252", "A364260" ]
null
Antti Karttunen, Jul 16 2023
2023-07-16T13:15:18
oeisdata/seq/A364/A364251.seq
4055000c4d8d5204773183494bed1924
A364252
a(n) = 1 if n has no other prime factors than 2 and/or Mersenne primes, otherwise 0.
[ "1", "1", "1", "1", "0", "1", "1", "1", "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "1", "1" ]
[ "nonn", "mult" ]
15
1
null
[ "A036987", "A209229", "A219174", "A336467", "A336923", "A364251", "A364252" ]
null
Antti Karttunen, Jul 16 2023
2023-07-16T16:24:24
oeisdata/seq/A364/A364252.seq
4b0cb35f77316f8716fbcd59c14df1e2
A364253
a(n) = n - A332215(n).
[ "1", "1", "0", "2", "-10", "0", "0", "4", "4", "-20", "-52", "0", "-242", "0", "-14", "8", "-494", "8", "-1004", "-40", "8", "-104", "-2024", "0", "2", "-484", "18", "0", "-4066", "-28", "0", "16", "-92", "-988", "8", "16", "-16346", "-2008", "-470", "-80", "-32726", "16", "-65492", "-208", "-12", "-4048", "-262096", "0", "38", "4", "-970", "-968", "-1048522", "36", "-64", "0", "-1988", "-8132", "-2097092", "-56", "-4194242", "0", "38", "32" ]
[ "sign" ]
12
1
4
[ "A332215", "A335431", "A364253", "A364254" ]
null
Antti Karttunen, Jul 16 2023
2023-07-16T20:32:19
oeisdata/seq/A364/A364253.seq
43aeda0a0ef783c670ec1af5e78e3ea5
A364254
a(n) = gcd(n, A332215(n)).
[ "1", "1", "3", "2", "5", "6", "7", "4", "1", "10", "1", "12", "1", "14", "1", "8", "1", "2", "1", "20", "1", "2", "23", "24", "1", "2", "9", "28", "1", "2", "31", "16", "1", "2", "1", "4", "1", "2", "1", "40", "1", "2", "1", "4", "3", "46", "1", "48", "1", "2", "1", "4", "1", "18", "1", "56", "1", "2", "1", "4", "1", "62", "1", "32", "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "15", "4", "1", "2", "1", "80", "1", "2", "1", "4", "5", "2", "1", "8", "1", "6", "13", "92", "1", "2", "1", "96", "1", "2", "3", "4" ]
[ "nonn" ]
9
1
3
[ "A332215", "A364253", "A364254", "A364255" ]
null
Antti Karttunen, Jul 16 2023
2023-07-16T20:32:23
oeisdata/seq/A364/A364254.seq
25d646cf2ead0f6bbbed0c3c8e19811c
A364255
a(n) = gcd(n, A163511(n)).
[ "1", "1", "2", "3", "4", "1", "6", "1", "8", "9", "2", "1", "12", "1", "2", "1", "16", "1", "18", "1", "4", "3", "2", "1", "24", "5", "2", "1", "4", "1", "2", "1", "32", "3", "2", "5", "36", "1", "2", "1", "8", "1", "6", "1", "4", "3", "2", "1", "48", "1", "10", "1", "4", "1", "2", "11", "8", "3", "2", "1", "4", "1", "2", "1", "64", "1", "6", "1", "4", "3", "10", "1", "72", "1", "2", "5", "4", "7", "2", "1", "16", "27", "2", "1", "12", "5", "2", "1", "8", "1", "6", "1", "4", "3", "2", "1", "96", "1", "2", "1", "20", "1", "2", "1", "8", "105" ]
[ "nonn" ]
21
0
3
[ "A163511", "A339969", "A364254", "A364255", "A364256", "A364257", "A364258", "A364491", "A364492", "A364493", "A364500", "A364949" ]
null
Antti Karttunen, Jul 16 2023
2023-09-01T15:23:26
oeisdata/seq/A364/A364255.seq
e18561369a4636f355955e067c0d49ed
A364256
a(n) = gcd(n, A243071(n)).
[ "1", "1", "3", "2", "1", "6", "1", "4", "1", "2", "1", "12", "1", "2", "1", "8", "1", "2", "1", "4", "1", "2", "1", "24", "1", "2", "9", "4", "1", "2", "1", "16", "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "43", "4", "5", "2", "1", "48", "1", "2", "1", "4", "1", "18", "1", "8", "1", "2", "1", "4", "1", "2", "3", "32", "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "3", "4", "11", "2", "1", "16", "1", "2", "1", "4", "1", "86", "1", "8", "1", "10", "7", "4", "1", "2", "1", "96", "1", "2", "11", "4" ]
[ "nonn" ]
12
1
3
[ "A243071", "A364254", "A364255", "A364256" ]
null
Antti Karttunen, Jul 17 2023
2023-07-17T18:00:00
oeisdata/seq/A364/A364256.seq
a79d4fb96ef4e63c01d1be5ab2589a15
A364257
Dirichlet inverse of A364255.
[ "1", "-2", "-3", "0", "-1", "6", "-1", "0", "0", "2", "-1", "0", "-1", "2", "5", "0", "-1", "0", "-1", "0", "3", "2", "-1", "0", "-4", "2", "26", "0", "-1", "-10", "-1", "0", "3", "2", "-3", "0", "-1", "2", "5", "0", "-1", "-6", "-1", "0", "-6", "2", "-1", "0", "0", "8", "5", "0", "-1", "-52", "-9", "0", "3", "2", "-1", "0", "-1", "2", "8", "0", "1", "-6", "-1", "0", "3", "6", "-1", "0", "-1", "2", "18", "0", "-5", "-10", "-1", "0", "-102", "2", "-1", "0", "-3", "2", "5", "0", "-1", "12" ]
[ "sign" ]
10
1
2
[ "A163511", "A323239", "A364255", "A364257" ]
null
Antti Karttunen, Jul 17 2023
2023-07-17T17:12:33
oeisdata/seq/A364/A364257.seq
a10cedf9b372489de598b150d9b253de
A364258
a(n) = A163511(n) - n.
[ "1", "1", "2", "0", "4", "4", "0", "-2", "8", "18", "8", "14", "0", "2", "-4", "-8", "16", "64", "36", "106", "16", "54", "28", "26", "0", "20", "4", "8", "-8", "-8", "-16", "-20", "32", "210", "128", "590", "72", "338", "212", "304", "32", "184", "108", "202", "56", "102", "52", "74", "0", "86", "40", "124", "8", "52", "16", "22", "-16", "6", "-16", "-4", "-32", "-28", "-40", "-50", "64", "664", "420", "3058", "256", "1806", "1180", "2330", "144", "1052", "676" ]
[ "sign", "look" ]
23
0
3
[ "A007283", "A163511", "A364255", "A364258", "A364287", "A364288", "A364292", "A364293", "A364294" ]
null
Antti Karttunen, Jul 25 2023
2023-07-26T14:32:59
oeisdata/seq/A364/A364258.seq
3b945f732d3f01fae8b61bfa3f67ea45
A364259
a(n) = A331410(A332212(n)).
[ "0", "0", "1", "0", "1", "1", "2", "0", "2", "1", "1", "1", "2", "2", "2", "0", "1", "2", "2", "1", "3", "1", "3", "1", "2", "2", "3", "2", "3", "2", "2", "0", "2", "1", "3", "2", "4", "2", "3", "1", "1", "3", "4", "1", "3", "3", "3", "1", "4", "2", "2", "2", "3", "3", "2", "2", "3", "3", "1", "2", "2", "2", "4", "0", "3", "2", "1", "1", "4", "3", "4", "2", "4", "4", "3", "2", "3", "3", "2", "1", "4", "1", "4", "3", "2", "4", "4", "1", "3", "3", "4", "3", "3", "3", "3", "1", "5", "4", "3", "2", "3", "2", "3", "2", "4" ]
[ "nonn" ]
11
1
7
[ "A000079", "A331410", "A332212", "A364259", "A364260" ]
null
Antti Karttunen, Jul 16 2023
2023-07-16T20:25:28
oeisdata/seq/A364/A364259.seq
2674187f23de31e1c468cb0697da2fe4
A364260
a(n) = A331410(A332214(n)).
[ "0", "0", "0", "1", "0", "2", "1", "1", "0", "3", "2", "2", "1", "2", "1", "2", "0", "4", "3", "3", "2", "3", "2", "4", "1", "3", "2", "3", "1", "3", "2", "1", "0", "5", "4", "4", "3", "4", "3", "6", "2", "4", "3", "5", "2", "5", "4", "2", "1", "4", "3", "4", "2", "4", "3", "3", "1", "4", "3", "2", "2", "2", "1", "2", "0", "6", "5", "5", "4", "5", "4", "8", "3", "5", "4", "7", "3", "7", "6", "3", "2", "5", "4", "6", "3", "6", "5", "4", "2", "6", "5", "3", "4", "3", "2", "4", "1", "5", "4", "5", "3", "5", "4", "5", "2", "5" ]
[ "nonn" ]
11
0
6
[ "A131577", "A163511", "A331410", "A332214", "A334204", "A335431", "A364259", "A364260" ]
null
Antti Karttunen, Jul 16 2023
2023-07-16T20:25:37
oeisdata/seq/A364/A364260.seq
11da7c3b56594afdf6c23709012cf594
A364261
a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared such that a(n-1) + a(n) has the same number of prime factors as a(n-1) * a(n).
[ "1", "2", "6", "10", "14", "13", "15", "3", "7", "19", "9", "11", "23", "4", "28", "53", "5", "17", "25", "35", "21", "27", "29", "34", "22", "38", "37", "26", "55", "33", "43", "31", "39", "49", "51", "41", "57", "59", "45", "99", "69", "47", "58", "46", "66", "30", "82", "71", "77", "61", "20", "44", "52", "12", "148", "68", "60", "196", "92", "36", "220", "212", "103", "62", "18", "78", "122", "73", "8", "127", "67", "79", "74", "97", "85" ]
[ "nonn" ]
14
1
2
[ "A001222", "A027746", "A364261", "A364262" ]
null
Scott R. Shannon, Jul 16 2023
2023-07-17T08:50:40
oeisdata/seq/A364/A364261.seq
80438d6a627b87ea5276da81336cef62
A364262
a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared such that a(n-1) + a(n) has the same number of distinct prime factors as a(n-1) * a(n).
[ "1", "2", "10", "4", "6", "8", "7", "3", "11", "9", "5", "13", "23", "16", "12", "24", "27", "17", "19", "25", "15", "51", "33", "37", "31", "32", "14", "46", "20", "22", "38", "28", "42", "18", "36", "30", "40", "26", "34", "44", "58", "29", "43", "35", "55", "47", "41", "53", "52", "50", "60", "45", "21", "39", "63", "49", "59", "64", "48", "57", "69", "61", "65", "67", "79", "73", "71", "81", "54", "56", "70", "80", "74", "76", "62", "68", "72" ]
[ "nonn" ]
14
1
2
[ "A001221", "A027748", "A364261", "A364262" ]
null
Scott R. Shannon, Jul 16 2023
2023-07-17T08:52:06
oeisdata/seq/A364/A364262.seq
2e1981b0e6a7fb3c16d2c4ce830a6050
A364263
Numbers j such that k=210*j, 2*k, k^2+k, k^2-k all are averages of twin primes.
[ "521457", "7235406", "107647749", "123718516", "161881498", "200141522", "215640361", "269177896", "301917955", "352021648", "393455227", "580398355", "716403116", "916268861", "1000979331", "1231997208", "1289093896", "1354550305", "1471667483", "1478187348", "1485031638", "1520586133" ]
[ "nonn" ]
42
1
1
[ "A363500", "A364263" ]
null
Bryce Case, Jr. and Antonio Gimenez, Jul 16 2023
2024-06-28T22:24:54
oeisdata/seq/A364/A364263.seq
059d8cb9e4b4824308a46a6e94487b1b
A364264
The Parker Square, read by rows.
[ "841", "1", "2209", "1681", "1369", "1", "529", "1681", "841" ]
[ "nonn", "tabf", "fini", "full" ]
33
1
1
[ "A308838", "A309810", "A348263", "A364264", "A379179" ]
null
Paolo Xausa, Jul 17 2023
2024-12-20T12:38:27
oeisdata/seq/A364/A364264.seq
8ec26140da68e112b818b78ed4613a42
A364265
The first term in a chain of at least 3 consecutive numbers each with exactly 6 distinct prime factors (i.e., belonging to A074969).
[ "323567034", "431684330", "468780388", "481098980", "577922904", "639336984", "715008644", "720990620", "726167154", "735965384", "769385252", "808810638", "822981560", "831034918", "839075510", "847765554", "879549670", "895723268", "902976710", "903293468", "904796814", "918520420", "940737005", "944087484", "982059364" ]
[ "nonn" ]
34
1
1
[ "A001221", "A001222", "A005117", "A007774", "A033992", "A033993", "A051270", "A074969", "A176655", "A246655", "A259349", "A273879", "A348072", "A348073", "A364265", "A364266" ]
null
R. J. Mathar, Jul 16 2023
2024-06-10T00:07:01
oeisdata/seq/A364/A364265.seq
445d3696c39b8f645096230ab26be3ac
A364266
The first term in a chain of at least 3 consecutive numbers each with exactly 5 distinct prime factors.
[ "1042404", "3460280", "3818828", "3998664", "4638984", "4991964", "5540248", "5701254", "5715500", "5964958", "6772050", "6794084", "7237384", "7453964", "7459088", "7745318", "7757034", "7993194", "8083634", "8153430", "8168194", "8273628", "8340834", "8340980", "8414756", "8486994", "8698898", "8722634", "8758904" ]
[ "nonn" ]
22
1
1
[ "A001221", "A006073", "A087978", "A140079", "A192203", "A364265", "A364266", "A364308", "A364309" ]
null
R. J. Mathar, Jul 16 2023
2024-10-01T03:33:10
oeisdata/seq/A364/A364266.seq
4aa83f25a037a208a0bc557e37bead79
A364267
Total number of blocks in all set partitions of [n] such that each element is contained in a block whose index parity coincides with the parity of the element.
[ "0", "1", "2", "5", "9", "24", "55", "169", "454", "1567", "4823", "18422", "63609", "265929", "1014266", "4595861", "19143089", "93286964", "420483103", "2189786125", "10601936382", "58688597511", "303349005967", "1776842374930", "9754696729753", "60223101819493", "349624680839546", "2267363687696309" ]
[ "nonn" ]
14
0
3
[ "A011655", "A274537", "A364267" ]
null
Alois P. Heinz, Jul 16 2023
2023-07-17T09:14:29
oeisdata/seq/A364/A364267.seq
ff5ea48261e3f338f43394b5ea57a270
A364268
a(n) = Sum_{k=1..n} k^2*sigma_2(k), where sigma_2 is A001157.
[ "1", "21", "111", "447", "1097", "2897", "5347", "10787", "18158", "31158", "45920", "76160", "104890", "153890", "212390", "299686", "383496", "530916", "661598", "879998", "1100498", "1395738", "1676108", "2165708", "2572583", "3147183", "3744963", "4568163", "5276285", "6446285", "7370767", "8768527", "10097107" ]
[ "nonn", "easy" ]
30
1
2
[ "A000330", "A001157", "A356125", "A364268", "A364269" ]
null
Seiichi Manyama, Oct 20 2023
2023-10-22T00:46:19
oeisdata/seq/A364/A364268.seq
a9b01bdec69d68c343c946e9ecdf76d1
A364269
a(n) = Sum_{k=1..n} k^3*sigma_2(k), where sigma_2 is A001157.
[ "1", "41", "311", "1655", "4905", "15705", "32855", "76375", "142714", "272714", "435096", "797976", "1171466", "1857466", "2734966", "4131702", "5556472", "8210032", "10692990", "15060990", "19691490", "26186770", "32635280", "44385680", "54557555", "69497155", "85637215", "108686815", "129222353", "164322353" ]
[ "nonn", "easy" ]
32
1
2
[ "A000537", "A001157", "A356125", "A364268", "A364269" ]
null
Seiichi Manyama, Oct 20 2023
2023-10-22T00:45:11
oeisdata/seq/A364/A364269.seq
05ce1ccbe8508e1d18d527d6db7dc08d
A364270
a(n) = 2^^n + 3^^n, where ^^ indicates tetration.
[ "2", "5", "31", "7625597485003" ]
[ "nonn", "base", "hard" ]
23
0
1
[ "A004249", "A014221", "A014222", "A321312", "A364270" ]
null
Marco Ripà, Oct 20 2023
2023-12-12T20:58:46
oeisdata/seq/A364/A364270.seq
5a9c5e7508b51e769d6fd68614abc4a3
A364271
Initial digit of n^((n + 1)^(n + 2)).
[ "0", "1", "2", "3", "1", "7", "1", "7", "2", "8", "1", "1", "1", "2", "7", "1", "9", "1", "2", "2", "4", "5", "1", "7", "3", "2", "4", "1", "2", "6", "2", "1", "2", "2", "1", "8", "1", "6", "1", "5", "2", "8", "8", "3", "9", "3", "4", "2", "4", "3", "1", "6", "2", "1", "6", "6", "9", "1", "9", "2", "5", "2", "9", "9", "6", "8", "4", "2", "7", "7", "6", "1", "2", "2", "3", "1", "2", "6", "1", "1", "6", "1", "1", "2", "3", "5", "1" ]
[ "nonn", "base" ]
20
0
3
[ "A000030", "A030198", "A364271", "A365689" ]
null
Marco Ripà, Oct 20 2023
2024-12-19T11:45:36
oeisdata/seq/A364/A364271.seq
553587f0b5fc712ea0db6be2c9672ac2
A364272
Number of strict integer partitions of n containing the sum of some subset of the parts. A variation of sum-full strict partitions.
[ "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "3", "1", "4", "3", "8", "6", "11", "10", "17", "16", "26", "25", "39", "39", "54", "60", "82", "84", "116", "126", "160", "177", "222", "242", "302", "337", "402", "453", "542", "601", "722", "803", "936", "1057", "1234", "1373", "1601", "1793", "2056", "2312", "2658", "2950", "3395", "3789", "4281", "4814", "5452", "6048" ]
[ "nonn" ]
8
0
11
[ "A000009", "A000041", "A007865", "A008284", "A008289", "A025065", "A085489", "A093971", "A108917", "A111133", "A151897", "A236912", "A237113", "A237667", "A237668", "A240861", "A275972", "A299702", "A320340", "A320347", "A323092", "A325862", "A363225", "A363226", "A364272", "A364346", "A364349", "A364350", "A364531", "A364532", "A364533", "A364534", "A364670" ]
null
Gus Wiseman, Aug 01 2023
2023-08-03T09:04:15
oeisdata/seq/A364/A364272.seq
aa3e45f915593c846f19957df4840b64
A364273
Number of chordless cycles (with length >= 4) in the complement of the n X n X n grid graph.
[ "0", "6", "780", "7992", "39339", "134754", "369918", "873000", "1844637", "3581154", "6501024", "11174568", "18356895", "29024082", "44412594", "66061944", "95860593", "136095090", "189502452", "259325784", "349373139", "464079618", "608572710", "788740872", "1011305349", "1283895234", "1615125768", "2014679880" ]
[ "nonn" ]
22
1
2
null
null
Eric W. Weisstein, Jul 17 2023
2025-02-16T08:34:06
oeisdata/seq/A364/A364273.seq
1050ffe0275eb8ff70b9b3622d117362
A364274
Lexicographically earliest sequence of distinct positive terms such that the cumulative sum Q(n) of the first n terms of the sequence has distinct digits.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "11", "12", "10", "13", "14", "15", "16", "17", "19", "18", "20", "21", "22", "23", "25", "24", "26", "27", "28", "29", "30", "31", "32", "33", "35", "34", "40", "36", "37", "38", "39", "41", "42", "43", "77", "44", "136", "45", "46", "48", "47", "49", "51", "50", "53", "55", "56", "57", "60", "52", "54", "58", "59", "61", "63", "134", "64", "65", "66", "67", "68" ]
[ "base", "nonn" ]
13
1
2
[ "A364274", "A364275" ]
null
Eric Angelini, Jul 17 2023
2023-08-02T11:54:57
oeisdata/seq/A364/A364274.seq
1e0504702bff195934b22d19dd04ef55
A364275
Lexicographically earliest sequence of distinct positive terms such that the cumulative sum Q(n) of the first n terms of the sequence has at least one duplicated digit.
[ "11", "22", "33", "34", "1", "9", "2", "3", "4", "12", "10", "14", "6", "5", "15", "7", "23", "13", "8", "20", "25", "26", "19", "16", "17", "18", "27", "24", "21", "29", "31", "28", "32", "30", "38", "35", "39", "37", "43", "41", "40", "51", "36", "42", "44", "47", "45", "46", "48", "50", "53", "58", "52", "54", "56", "49", "57", "55", "59", "61", "60", "64", "65", "62", "69", "63", "66", "72", "68", "74" ]
[ "base", "nonn" ]
8
1
1
[ "A364274", "A364275" ]
null
Eric Angelini, Jul 17 2023
2023-08-02T11:55:13
oeisdata/seq/A364/A364275.seq
0d5e06e2341fbb093ac82a281da1db0f
A364276
A 5 X 5 magic square of squares with the smallest possible magic sum, read by rows.
[ "1", "4", "961", "9", "400", "484", "256", "169", "25", "441", "121", "529", "100", "576", "49", "144", "225", "81", "729", "196", "625", "361", "64", "36", "289" ]
[ "nonn", "tabf", "fini", "full" ]
11
1
2
[ "A272932", "A358445", "A359383", "A364276" ]
null
Paolo Xausa, Jul 17 2023
2023-08-02T14:12:36
oeisdata/seq/A364/A364276.seq
640fefce79af040e15b13c9f4ef4f816
A364277
Number of permutations of [n] such that no cycle contains its length as an element.
[ "1", "0", "0", "1", "4", "24", "138", "1032", "8160", "75600", "751680", "8436960", "100679040", "1327052160", "18525024000", "280451808000", "4477627123200", "76690072166400", "1377634946688000", "26328977260185600", "525869478021888000", "11092929741653760000", "243781091314016256000", "5628622656645660672000" ]
[ "nonn" ]
13
0
5
[ "A362362", "A363881", "A364277", "A364279", "A364406" ]
null
Alois P. Heinz, Jul 17 2023
2023-07-23T17:02:34
oeisdata/seq/A364/A364277.seq
c3c4ccd8276d18260b72777673858a8c
A364278
Number of partitions of [n] with distinct block sizes such that no block contains its size as an element.
[ "1", "0", "0", "1", "1", "4", "24", "47", "153", "669", "5628", "13554", "61747", "247170", "1539565", "16979571", "53166394", "268393296", "1382097160", "7831424654", "59720804940", "917256305956", "3326800474687", "20441030261195", "112690616749302", "773175024537549", "5164903931159843", "52976603588044961" ]
[ "nonn" ]
8
0
6
[ "A326493", "A363881", "A364278", "A364279" ]
null
Alois P. Heinz, Jul 17 2023
2023-07-17T12:37:07
oeisdata/seq/A364/A364278.seq
a5b19369fab23bbd120ed7b570857092
A364279
Number of permutations of [n] with distinct cycle lengths such that no cycle contains its length as an element.
[ "1", "0", "0", "1", "2", "12", "86", "546", "4284", "39588", "416988", "4378848", "54297504", "695592000", "9840307680", "149031686880", "2387863575360", "40338090711360", "736126007279040", "13938942123429120", "279358800902737920", "5894877845100625920", "129943826126987765760", "2985640822908446976000" ]
[ "nonn" ]
15
0
5
[ "A000009", "A007838", "A362362", "A364277", "A364278", "A364279", "A364281", "A364406" ]
null
Alois P. Heinz, Jul 17 2023
2023-07-23T17:03:01
oeisdata/seq/A364/A364279.seq
4c80f9c58bea8c6d446293e7d3c56a52
A364280
Lexicographically earliest sequence of distinct positive integers such that a(n) is the least novel multiple of m, the product of all primes q < gpf(a(n-2)*a(n-1)) which do not divide a(n-2)*a(n-1); a(1) = 1, a(2) = 2.
[ "1", "2", "3", "4", "5", "6", "7", "10", "9", "8", "11", "105", "12", "13", "385", "18", "14", "15", "16", "17", "15015", "20", "19", "51051", "30", "21", "22", "25", "42", "23", "230945", "84", "24", "35", "26", "33", "70", "27", "28", "40", "36", "29", "37182145", "48", "31", "1078282205", "54", "32", "34", "30030", "37", "6678671", "60060", "38", "51", "5005", "44", "39" ]
[ "nonn" ]
16
1
2
[ "A002110", "A007947", "A359804", "A364154", "A364280" ]
null
David James Sycamore, Jul 17 2023
2025-04-13T07:11:38
oeisdata/seq/A364/A364280.seq
2b8db4af88e6169f7647861fea780756
A364281
Number of permutations of [n] with distinct cycle lengths such that each cycle contains exactly one cycle length as an element.
[ "1", "1", "1", "4", "10", "48", "252", "1584", "10800", "93600", "823680", "8588160", "93381120", "1158312960", "14805504000", "215028172800", "3159494553600", "51973589606400", "873152856576000", "16058241239040000", "300754643245056000", "6159522883497984000", "127439374149255168000" ]
[ "nonn" ]
20
0
4
[ "A327712", "A364279", "A364281", "A364406" ]
null
Alois P. Heinz, Jul 17 2023
2025-05-23T04:12:30
oeisdata/seq/A364/A364281.seq
6bf251f856aeae8dd9327e0011609cdf
A364282
Number of partitions of [n] with distinct block sizes such that each block contains exactly one block size different from its own as an element.
[ "1", "0", "0", "1", "1", "4", "11", "24", "52", "226", "969", "2281", "8960", "29898", "193202", "1075509", "3346852", "14280775", "75858992", "332978617", "2839114204", "19507400962", "75453432614", "383685116089", "2030801987312", "14025840725149", "77948290561659", "884660446815877", "7273497958681824" ]
[ "nonn" ]
17
0
6
[ "A000110", "A000166", "A007837", "A363881", "A364207", "A364278", "A364282", "A364283" ]
null
Alois P. Heinz, Jul 17 2023
2023-07-18T08:57:34
oeisdata/seq/A364/A364282.seq
be28b5414907686ecd344d271f32e1e4
A364283
Number of permutations of [n] with distinct cycle lengths such that each cycle contains exactly one cycle length different from its own as an element.
[ "1", "0", "0", "1", "2", "12", "60", "408", "2640", "24480", "208080", "2262960", "23950080", "307359360", "3835641600", "57400358400", "825160089600", "13909727462400", "229664981145600", "4310966499840000", "79428141112320000", "1658163790483200000", "33795850208440320000", "770528520983789568000" ]
[ "nonn" ]
18
0
5
[ "A000009", "A000166", "A007838", "A362362", "A364277", "A364279", "A364281", "A364282", "A364283", "A364406" ]
null
Alois P. Heinz, Jul 17 2023
2023-07-23T17:04:02
oeisdata/seq/A364/A364283.seq
71515f3f37b103cc7a043ccd2a323e39
A364284
Numbers k such that A261627(k) = 1.
[ "5", "7", "10", "11", "12", "19", "22", "30", "34", "44", "46", "72", "142" ]
[ "nonn" ]
21
1
1
[ "A261627", "A261628", "A364284" ]
null
Jud McCranie, Aug 26 2023
2023-08-27T16:28:49
oeisdata/seq/A364/A364284.seq
0f00087c08a297d4dc067429cb646177
A364285
Number T(n,k) of partitions of n with largest part k where each block of part i with multiplicity j is marked with a word of length i*j over an n-ary alphabet whose letters appear in alphabetical order and all n letters occur exactly once in the partition; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
[ "1", "0", "1", "0", "1", "1", "0", "1", "3", "1", "0", "1", "7", "4", "1", "0", "1", "15", "20", "5", "1", "0", "1", "31", "81", "30", "6", "1", "0", "1", "63", "287", "175", "42", "7", "1", "0", "1", "127", "952", "841", "280", "56", "8", "1", "0", "1", "255", "3025", "4545", "1638", "420", "72", "9", "1", "0", "1", "511", "9370", "23820", "10333", "2730", "600", "90", "10", "1" ]
[ "nonn", "tabl" ]
24
0
9
[ "A000007", "A000225", "A057427", "A178682", "A364285", "A364310", "A364322" ]
null
Alois P. Heinz, Jul 17 2023
2023-07-20T09:43:38
oeisdata/seq/A364/A364285.seq
e3d57916815dded9fdb7f930032e48ff
A364286
Composite numbers k for which A324644(k)/A324198(k) = 2.
[ "33", "51", "69", "91", "99", "135", "141", "145", "153", "159", "187", "207", "213", "217", "285", "295", "303", "321", "339", "391", "411", "423", "427", "435", "445", "477", "507", "519", "573", "637", "639", "679", "681", "699", "771", "783", "799", "843", "855", "861", "885", "895", "901", "909", "933", "951", "963", "1017", "1041", "1057", "1059", "1071", "1081", "1083", "1147", "1149", "1173", "1185", "1195", "1203", "1207" ]
[ "nonn" ]
23
1
1
[ "A000203", "A082686", "A276086", "A324198", "A324644", "A332458", "A349169", "A351458", "A364286", "A371082" ]
null
Antti Karttunen, Jul 17 2023
2024-03-10T20:01:30
oeisdata/seq/A364/A364286.seq
0f7299c3c4830bc9fca3dcdabc99e729
A364287
Numbers k such that A163511(k) < k.
[ "7", "14", "15", "28", "29", "30", "31", "56", "58", "59", "60", "61", "62", "63", "112", "116", "118", "119", "120", "121", "122", "123", "124", "125", "126", "127", "223", "224", "232", "236", "238", "239", "240", "242", "244", "245", "246", "247", "248", "249", "250", "251", "252", "253", "254", "255", "383", "446", "447", "448", "464", "472", "476", "478", "479", "480", "484", "488", "490", "492", "493", "494", "495", "496", "497", "498" ]
[ "nonn" ]
6
1
1
[ "A163511", "A364258", "A364287", "A364289", "A364290" ]
null
Antti Karttunen, Jul 25 2023
2023-07-25T12:30:53
oeisdata/seq/A364/A364287.seq
37aa45ce053c0003f275c7395c9e1235
A364288
a(n) = n - A243071(n).
[ "1", "1", "0", "2", "-2", "0", "-8", "4", "4", "-4", "-20", "0", "-50", "-16", "2", "8", "-110", "8", "-236", "-8", "-8", "-40", "-488", "0", "14", "-100", "18", "-32", "-994", "4", "-2016", "16", "-28", "-220", "8", "16", "-4058", "-472", "-86", "-16", "-8150", "-16", "-16340", "-80", "20", "-976", "-32720", "0", "26", "28", "-202", "-200", "-65482", "36", "-4", "-64", "-452", "-1988", "-131012", "8", "-262082", "-4032", "6", "32", "-58", "-56" ]
[ "sign" ]
13
1
4
[ "A007283", "A243071", "A364253", "A364256", "A364258", "A364288", "A364289", "A364290", "A364291" ]
null
Antti Karttunen, Jul 25 2023
2023-07-25T13:11:23
oeisdata/seq/A364/A364288.seq
8a5dc90e7596db200d4b696d29ae7318
A364289
Numbers k such that A243071(k) >= k.
[ "3", "5", "6", "7", "10", "11", "12", "13", "14", "17", "19", "20", "21", "22", "23", "24", "26", "28", "29", "31", "33", "34", "37", "38", "39", "40", "41", "42", "43", "44", "46", "47", "48", "51", "52", "53", "55", "56", "57", "58", "59", "61", "62", "65", "66", "67", "68", "69", "71", "73", "74", "76", "78", "79", "80", "82", "83", "84", "85", "86", "87", "88", "89", "91", "92", "93", "94", "95", "96", "97", "99", "101", "102", "103", "104", "106", "107", "109" ]
[ "nonn" ]
7
1
1
[ "A007283", "A243071", "A364287", "A364288", "A364289", "A364290" ]
null
Antti Karttunen, Jul 25 2023
2023-07-25T12:31:05
oeisdata/seq/A364/A364289.seq
6ae6f10161b24ce246c48d1bfc62404b
A364290
Numbers k such that A243071(k) < k.
[ "1", "2", "4", "8", "9", "15", "16", "18", "25", "27", "30", "32", "35", "36", "45", "49", "50", "54", "60", "63", "64", "70", "72", "75", "77", "81", "90", "98", "100", "105", "108", "120", "121", "125", "126", "128", "135", "140", "143", "144", "147", "150", "154", "162", "165", "169", "175", "180", "189", "196", "200", "210", "216", "225", "231", "240", "242", "243", "245", "250", "252", "256", "270", "273", "275", "280", "286", "288", "289", "294" ]
[ "nonn" ]
8
1
2
[ "A243071", "A364287", "A364288", "A364289", "A364290", "A364291" ]
null
Antti Karttunen, Jul 25 2023
2023-07-25T12:31:12
oeisdata/seq/A364/A364290.seq
4bb5674122f6fee32e2eafeafdd1cad0
A364291
Numbers k such that A243071(k) <= k.
[ "1", "2", "3", "4", "6", "8", "9", "12", "15", "16", "18", "24", "25", "27", "30", "32", "35", "36", "45", "48", "49", "50", "54", "60", "63", "64", "70", "72", "75", "77", "81", "90", "96", "98", "100", "105", "108", "120", "121", "125", "126", "128", "135", "140", "143", "144", "147", "150", "154", "162", "165", "169", "175", "180", "189", "192", "196", "200", "210", "216", "225", "231", "240", "242", "243", "245", "250", "252", "256", "270", "273" ]
[ "nonn" ]
6
1
2
[ "A007283", "A243071", "A364287", "A364288", "A364290", "A364291" ]
null
Antti Karttunen, Jul 25 2023
2023-07-25T12:31:20
oeisdata/seq/A364/A364291.seq
4c2f49fcc5b50c8f7b5c5c529b354e38
A364292
Numbers k such that A163511(k) <= k.
[ "3", "6", "7", "12", "14", "15", "24", "28", "29", "30", "31", "48", "56", "58", "59", "60", "61", "62", "63", "96", "112", "116", "118", "119", "120", "121", "122", "123", "124", "125", "126", "127", "192", "223", "224", "232", "236", "238", "239", "240", "242", "244", "245", "246", "247", "248", "249", "250", "251", "252", "253", "254", "255", "383", "384", "446", "447", "448", "464", "472", "476", "478", "479", "480", "484", "488", "490", "492" ]
[ "nonn" ]
9
1
1
[ "A007283", "A163511", "A364258", "A364287", "A364289", "A364292", "A364293" ]
null
Antti Karttunen, Jul 25 2023
2023-07-26T08:30:42
oeisdata/seq/A364/A364292.seq
6efba49dca64de57f4627856f904a8be
A364293
Odd numbers k for which A163511(k) <= k.
[ "3", "7", "15", "29", "31", "59", "61", "63", "119", "121", "123", "125", "127", "223", "239", "245", "247", "249", "251", "253", "255", "383", "447", "479", "493", "495", "497", "499", "501", "503", "505", "507", "509", "511", "767", "895", "957", "959", "989", "991", "999", "1001", "1003", "1005", "1007", "1009", "1011", "1013", "1015", "1017", "1019", "1021", "1023", "1535", "1789", "1791", "1917", "1919", "1977", "1979", "1981" ]
[ "nonn" ]
10
1
1
[ "A000225", "A163511", "A364258", "A364292", "A364293", "A364294" ]
null
Antti Karttunen, Jul 25 2023
2023-07-26T08:30:04
oeisdata/seq/A364/A364293.seq
36e02f5e4457efa30b8926854dacb973
A364294
Difference k - A163511(k) computed for those odd numbers k for which the difference is nonnegative.
[ "0", "2", "8", "8", "20", "4", "28", "50", "28", "22", "58", "86", "110", "2", "52", "50", "128", "132", "166", "202", "236", "22", "124", "232", "136", "286", "146", "74", "246", "370", "352", "412", "452", "488", "238", "458", "216", "568", "362", "692", "68", "236", "338", "606", "754", "550", "536", "728", "854", "846", "904", "952", "994", "694", "478", "1124", "744", "1368", "96", "484", "1084", "1490", "10", "236", "812", "746", "1254" ]
[ "nonn", "look" ]
22
1
2
[ "A007283", "A163511", "A364258", "A364293", "A364294" ]
null
Antti Karttunen, Jul 25 2023
2023-07-26T14:33:16
oeisdata/seq/A364/A364294.seq
615c48122aa2d2823b524c3aa3d44c2e
A364295
Numbers k such that A292943(k) = A292944(k).
[ "1", "2", "3", "4", "6", "8", "9", "12", "16", "18", "24", "32", "36", "45", "48", "64", "72", "90", "96", "128", "144", "165", "180", "189", "192", "256", "288", "330", "360", "378", "384", "512", "576", "660", "720", "756", "768", "1024", "1152", "1320", "1440", "1512", "1536", "2048", "2304", "2640", "2880", "3024", "3072", "4096", "4608", "5280", "5760", "6048", "6144", "8192", "9216", "10560", "11520", "12096", "12288", "16384" ]
[ "nonn" ]
11
1
2
[ "A000079", "A007283", "A029744", "A163511", "A243071", "A292943", "A292944", "A364295", "A364296", "A364494", "A364496" ]
null
Antti Karttunen, Jul 26 2023
2023-07-27T15:31:17
oeisdata/seq/A364/A364295.seq
acb2f44e1533cf7c80cb92d2fc3247d6
A364296
Odd numbers k for which A292943(k) == A292944(k).
[ "1", "3", "9", "45", "165", "189", "114595", "330993", "1277601" ]
[ "nonn", "more" ]
9
1
2
[ "A163511", "A243071", "A292943", "A292944", "A364295", "A364296", "A364495" ]
null
Antti Karttunen, Jul 27 2023
2023-07-27T15:31:22
oeisdata/seq/A364/A364296.seq
c7359da05624fae74e00eb69049f023b
A364297
a(n) = A348717(A163511(n)).
[ "1", "2", "4", "2", "8", "4", "6", "2", "16", "8", "18", "4", "12", "6", "10", "2", "32", "16", "54", "8", "36", "18", "50", "4", "24", "12", "30", "6", "20", "10", "14", "2", "64", "32", "162", "16", "108", "54", "250", "8", "72", "36", "150", "18", "100", "50", "98", "4", "48", "24", "90", "12", "60", "30", "70", "6", "40", "20", "42", "10", "28", "14", "22", "2", "128", "64", "486", "32", "324", "162", "1250", "16", "216", "108", "750", "54", "500", "250", "686", "8", "144" ]
[ "nonn" ]
34
0
2
[ "A000265", "A000668", "A007283", "A163511", "A243071", "A245611", "A245612", "A278531", "A286531", "A348717", "A364297", "A364949", "A364956", "A364959", "A364963", "A365423" ]
null
Antti Karttunen, Aug 15 2023
2023-09-06T06:58:32
oeisdata/seq/A364/A364297.seq
f5350d16c4f418d0b47e6109b59a67bd
A364298
Square array read by ascending antidiagonals: T(n,k) = [x^k] 1/(1 + x) * Legendre_P(k, (1 - x)/(1 + x))^(-n) for n >= 1, k >= 0.
[ "1", "1", "1", "1", "3", "19", "1", "5", "73", "721", "1", "7", "163", "3747", "49251", "1", "9", "289", "10805", "329001", "5370751", "1", "11", "451", "23623", "1179251", "44127003", "859748023", "1", "13", "649", "43929", "3100001", "190464755", "8405999785", "190320431953", "1", "15", "883", "73451", "6751251", "589050007", "42601840975", "2160445363107" ]
[ "nonn", "tabl", "easy" ]
8
1
5
[ "A005258", "A005259", "A143007", "A364113", "A364298", "A364299", "A364300", "A364301", "A364302" ]
null
Peter Bala, Jul 18 2023
2023-07-20T10:10:40
oeisdata/seq/A364/A364298.seq
f84a296b06bcd5fb6ff9d719b6e611c7
A364299
a(n) = [x^n] 1/(1 + x) * Legendre_P(n, (1 - x)/(1 + x))^(-1) for n >= 0.
[ "1", "1", "19", "721", "49251", "5370751", "859748023", "190320431953", "55743765411043", "20884452115700251", "9745388924112505269", "5543574376457462884111", "3776677001062829977964007", "3036161801705682492174749691", "2844274879825369072829081331519" ]
[ "nonn", "easy" ]
8
0
3
[ "A005258", "A364298", "A364299", "A364300", "A364301", "A364302" ]
null
Peter Bala, Jul 18 2023
2023-07-20T10:08:59
oeisdata/seq/A364/A364299.seq
cdfc0a71d94857f493ffec1e9b22232a
A364300
a(n) = [x^n] 1/(1 + x) * Legendre_P(n, (1 - x)/(1 + x))^(-2) for n >= 0.
[ "1", "3", "73", "3747", "329001", "44127003", "8405999785", "2160445363107", "720972846685225", "303256387595475003", "157007652309393485073", "98141188253799911132091", "72882030213423405890701449", "63436168183711463443127520699", "63968150042375034921379294100073", "73985402858435691329113991048739747" ]
[ "nonn", "easy" ]
7
0
2
[ "A005259", "A364298", "A364299", "A364300", "A364301", "A364302" ]
null
Peter Bala, Jul 18 2023
2023-07-20T10:09:34
oeisdata/seq/A364/A364300.seq
fa04557d6dcde0c0f5b033a911823a07