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1999-12-11 03:00:00
2025-04-28 00:58:08
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A381215
Numbers k such that the difference between the largest and smallest element of the set of bases and exponents (including exponents = 1) in the prime factorization of k is 1.
[ "2", "8", "9", "36", "72", "81", "108", "216", "625", "15625", "117649", "5764801", "25937424601", "3138428376721", "23298085122481", "3937376385699289", "48661191875666868481", "14063084452067724991009", "104127350297911241532841", "37589973457545958193355601", "907846434775996175406740561329" ]
[ "nonn", "easy" ]
19
1
1
[ "A036878", "A081812", "A104126", "A381212", "A381214", "A381215", "A381317" ]
null
Paolo Xausa, Feb 19 2025
2025-02-21T09:31:32
oeisdata/seq/A381/A381215.seq
b564d8072b905fb19a234b74470bdb80
A381216
Number of isomers of C_n H_{2n+2} O_2.
[ "1", "2", "5", "11", "28", "69", "179", "463", "1225", "3246", "8697", "23366", "63137", "171051", "465002", "1266831", "3459262", "9462393", "25926939", "71139400", "195451500", "537608802", "1480316960", "4079977874", "11254956840", "31072771980", "85850016944", "237356027117", "656657132953", "1817758531055", "5034725293449" ]
[ "nonn" ]
10
0
2
[ "A000598", "A000599", "A000600", "A000602", "A000635", "A000636", "A381216" ]
null
Erich Friedman, Feb 17 2025
2025-02-18T19:40:35
oeisdata/seq/A381/A381216.seq
2b1fed5362cf3c26ddb2c9736abe5747
A381217
a(n) is the least positive k such that the sum of the reverses of the first k primes is divisible by n.
[ "1", "1", "10", "5", "2", "16", "5", "20", "20", "3", "9", "16", "7", "5", "10", "30", "4", "20", "68", "44", "16", "20", "9", "20", "19", "7", "26", "5", "47", "34", "19", "30", "20", "28", "99", "20", "29", "68", "54", "44", "86", "16", "41", "20", "74", "26", "40", "30", "16", "50", "28", "82", "97", "26", "101", "51", "68", "47", "6", "44", "38", "53", "42", "30", "7", "20", "38", "28", "10", "99", "110", "20", "72", "121", "103", "137", "189" ]
[ "nonn", "base" ]
13
1
3
[ "A071602", "A381217" ]
null
Robert Israel, Feb 17 2025
2025-02-19T11:21:03
oeisdata/seq/A381/A381217.seq
f9abbd4c8c1945fe8c8094814f550595
A381218
Odd numbers with both an odd number of prime factors (counted with multiplicity) and an odd number of distinct prime factors. (Intersection of A067019 and A098903.)
[ "3", "5", "7", "11", "13", "17", "19", "23", "27", "29", "31", "37", "41", "43", "47", "53", "59", "61", "67", "71", "73", "79", "83", "89", "97", "101", "103", "105", "107", "109", "113", "125", "127", "131", "137", "139", "149", "151", "157", "163", "165", "167", "173", "179", "181", "191", "193", "195", "197", "199", "211", "223", "227", "229", "231", "233", "239" ]
[ "nonn", "easy" ]
8
1
1
[ "A067019", "A098903", "A381218" ]
null
Harvey P. Dale, Feb 17 2025
2025-02-17T13:01:58
oeisdata/seq/A381/A381218.seq
aaa305d71970361857c2f1084768b957
A381219
a(n) = (6^n+2^n-2*3^n)*(n-1)!/2.
[ "1", "11", "170", "3450", "87864", "2715720", "99248400", "4200210000", "202383054720", "10949741066880", "657619863264000", "43423960900320000", "3127284944109849600", "243957907264508236800", "20493712266753293568000", "1844490309401727187200000", "177073768932670444843008000", "18061662138488384327847936000", "1950666948832313303630438400000" ]
[ "nonn" ]
11
1
2
[ "A379809", "A381219" ]
null
N. J. A. Sloane, Feb 17 2024, based on an email from David Broadhurst.
2025-02-18T15:34:59
oeisdata/seq/A381/A381219.seq
3e5d0547acbdffe21b93cfd6f8bd2c05
A381220
First differences of A381116.
[ "6", "3", "7", "7", "6", "11", "8", "8", "1", "15", "12", "9", "13", "10", "19", "7", "18", "11", "18", "5", "22", "12", "21", "3", "20", "11", "35", "5", "16", "18", "18", "23", "17", "20", "26", "17", "3", "42", "4", "7", "42", "22", "25", "1", "34", "9", "8", "47", "6", "55", "8", "49", "7", "8", "6", "42", "14", "32", "19", "6", "51", "2", "50", "11", "27", "42", "25", "46", "54", "21", "22", "45", "4", "16", "53", "4", "73", "10", "25", "39", "9", "70", "11", "46", "33", "49", "27", "11", "20", "17" ]
[ "nonn" ]
8
1
1
[ "A381019", "A381116", "A381220", "A381221" ]
null
N. J. A. Sloane, Feb 18 2025
2025-02-18T10:22:00
oeisdata/seq/A381/A381220.seq
2e3ad7b259f4a940170f6245e6b28f8a
A381221
Partial sums of A381116.
[ "6", "9", "16", "23", "29", "40", "48", "56", "57", "72", "84", "93", "106", "116", "135", "142", "160", "171", "189", "194", "216", "228", "249", "252", "272", "283", "318", "323", "339", "357", "375", "398", "415", "435", "461", "478", "481", "523", "527", "534", "576", "598", "623", "624", "658", "667", "675", "722", "728", "783", "791", "840", "847", "855", "861", "903", "917", "949", "968", "974", "1025", "1027", "1077", "1088", "1115", "1157" ]
[ "nonn" ]
6
1
1
null
null
N. J. A. Sloane, Feb 18 2025
2025-02-18T10:25:41
oeisdata/seq/A381/A381221.seq
b0467c8fc4377e11f97fa4d54602d081
A381222
Smallest number missing from A381019 after A381019(n) has been found.
[ "2", "3", "4", "4", "4", "4", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "18", "18", "18" ]
[ "nonn" ]
10
1
1
[ "A381019", "A381119", "A381222" ]
null
N. J. A. Sloane, Feb 19 2025
2025-02-20T04:45:30
oeisdata/seq/A381/A381222.seq
edac3d382155a32ca9cf4358dc205838
A381223
Take the list (A381222) of successive values of the smallest number missing from A381019, and keep just the first of any run of successive equal terms.
[ "2", "3", "4", "6", "10", "14", "18", "24", "26", "30", "34", "36", "42", "44", "45", "46", "50", "52", "54", "56", "58", "60", "66", "72", "76", "78", "84", "90", "96", "100", "102", "108", "110", "112", "114", "120", "122", "124", "126", "130", "136", "138", "144", "150", "156", "160", "162", "168", "170", "172", "174", "176", "180", "186", "188", "190", "192" ]
[ "nonn" ]
11
1
1
[ "A381019", "A381222", "A381223" ]
null
N. J. A. Sloane, Feb 20 2025
2025-02-20T23:47:59
oeisdata/seq/A381/A381223.seq
901069acfc9263f74193b5cfe054422c
A381224
a(n) is the integer resulting from the concatenation of the unit digit of prime(n-1) to the digits of prime(n) without its own unit digit.
[ "0", "2", "3", "5", "71", "11", "31", "71", "92", "32", "93", "13", "74", "14", "34", "75", "35", "96", "16", "77", "17", "37", "98", "38", "99", "710", "110", "310", "710", "911", "312", "713", "113", "713", "914", "915", "115", "716", "316", "717", "317", "918", "119", "119", "319", "719", "921", "122", "322", "722", "923", "323", "924", "125", "125", "726", "326", "927", "127", "728", "128", "329", "330", "731", "131", "331", "733", "133", "734", "734", "935", "335" ]
[ "nonn", "base", "look" ]
19
1
2
[ "A000040", "A032759", "A290148", "A339467", "A381224" ]
null
N. J. A. Sloane, Feb 22 2025
2025-02-22T14:06:48
oeisdata/seq/A381/A381224.seq
f934688a9ab9764308f662a09f7668cd
A381225
Index of first occurrence of n in A290148.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "91", "101", "12", "22", "32", "42", "52", "62", "72", "82", "92", "201", "13", "23", "33", "43", "53", "63", "73", "83", "93", "301", "14", "24", "34", "44", "54", "64", "74", "84", "94", "401", "15", "25", "35", "45", "55", "65", "75", "85", "95", "501", "16", "26", "36", "46", "56", "66", "76", "86", "96", "601", "17", "27", "37", "47", "57", "67", "77", "87", "97", "701", "18", "28", "38", "48", "58", "68", "78", "88", "98", "801", "19", "29", "39" ]
[ "nonn", "base", "look" ]
10
0
2
[ "A290148", "A381225" ]
null
N. J. A. Sloane, Feb 23 2025
2025-02-23T09:02:58
oeisdata/seq/A381/A381225.seq
81056a8f9ad0d2f6eb122ac085aeb343
A381226
a(n) is the number of distinct positive integers that can be obtained by starting with n!, and optionally applying the operations square root, floor, and ceiling, in any order.
[ "1", "2", "4", "6", "7", "8", "8", "9", "10", "10", "10", "11", "12", "12", "12", "12", "12", "13", "13", "13", "14", "14", "14", "14", "14", "14", "14", "14", "15", "15", "15", "15", "15", "15", "16", "16", "16", "16", "16", "16", "16", "16", "16", "16", "16", "16", "16", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17", "18", "18", "18", "18", "18", "18", "18", "18", "18", "18", "18" ]
[ "nonn" ]
33
1
2
[ "A000319", "A139004", "A381226", "A381227", "A381229" ]
null
N. J. A. Sloane, Feb 24 2025
2025-03-16T12:55:32
oeisdata/seq/A381/A381226.seq
bc6b3210cbb9bfe6bd5c0b79b712a116
A381227
Irregular triangle read by rows: row n lists the A381226(n) numbers constructed in the definition of A381226, in increasing order.
[ "1", "1", "2", "1", "2", "3", "6", "1", "2", "3", "4", "5", "24", "1", "2", "3", "4", "10", "11", "120", "1", "2", "3", "5", "6", "26", "27", "720", "1", "2", "3", "8", "9", "70", "71", "5040", "1", "2", "3", "4", "14", "15", "200", "201", "40320", "1", "2", "3", "4", "5", "24", "25", "602", "603", "362880", "1", "2", "3", "6", "7", "43", "44", "1904", "1905", "3628800", "1", "2", "3", "8", "9", "79", "80", "6317", "6318", "39916800" ]
[ "nonn", "tabf" ]
14
1
3
[ "A139004", "A381226", "A381227", "A381228", "A381229" ]
null
N. J. A. Sloane, Feb 25 2025
2025-02-25T18:24:51
oeisdata/seq/A381/A381227.seq
95d9dba9051fd97597406b5ab233add7
A381228
Smallest k such that n appears in row k of the triangle in A381227, or -1 if n never appears in A381227.
[ "1", "2", "3", "4", "4", "3", "10", "7", "7", "5", "5", "12", "12", "8", "8", "13", "13", "21", "36", "22", "22", "37", "14", "4", "9", "6", "6", "39", "39", "24", "24", "15", "15", "69", "41", "41", "25", "25", "42", "42", "72", "72", "10", "10", "43", "16", "16", "74", "128", "44", "44", "75", "130", "76", "76", "27", "27", "77", "77", "134", "134", "78", "46", "46", "17", "17", "79", "79", "28" ]
[ "nonn" ]
12
1
2
[ "A139004", "A381226", "A381227", "A381228", "A381229" ]
null
N. J. A. Sloane, Feb 25 2025
2025-02-28T05:13:29
oeisdata/seq/A381/A381228.seq
2c7107a4b37f0a04fdced506863bf564
A381229
a(n) is the number of distinct positive integers that can be obtained by starting with n, and optionally applying the operations square root, floor, and ceiling, in any order.
[ "1", "2", "3", "3", "4", "4", "4", "4", "4", "5", "5", "5", "5", "5", "5", "4", "6", "6", "6", "6", "6", "6", "6", "6", "5", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "5", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "5", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "5", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "5", "7", "7", "7", "7", "7", "7" ]
[ "nonn" ]
8
1
2
[ "A381226", "A381227", "A381228", "A381229" ]
null
N. J. A. Sloane and Jinyuan Wang, Feb 25 2025
2025-02-25T15:05:36
oeisdata/seq/A381/A381229.seq
f045c8800bfcf78e74b5d323dbcc10d0
A381230
Index of first occurrence of n in A000319, or -1 if n never appears there.
[ "6", "0", "17", "45", "13", "42", "938", "920", "57403", "7865", "15862", "313445", "54988", "53976", "57573", "61372", "83445", "14998", "360213", "57322", "59858", "2070497", "2021631", "14918", "58001", "1394543", "79664", "2056395", "85989", "11", "8", "71662", "5495575", "5652770", "360110", "2070250", "5947332", "5514279", "5514772", "2015129", "78877", "305403", "1031", "1869352", "5652707", "4823241" ]
[ "nonn" ]
51
0
1
[ "A000319", "A381230", "A381231" ]
null
N. J. A. Sloane, Feb 28 2025
2025-03-14T02:34:32
oeisdata/seq/A381/A381230.seq
a33ca61aff824b81aac6c97acbe553e2
A381231
Index of first occurrence of -n in A000319, or -1 if -n never appears there.
[ "6", "3", "4", "5", "48", "15642", "14", "87", "924", "23", "1074", "1066", "14524", "7051", "15000", "71709", "57604", "57554", "2056626", "2036049", "16068", "86", "934", "37142", "57439", "72635", "57342", "1394559", "358329", "2112076", "16941", "2015018", "57124", "27572", "1837444", "29", "2058540", "54694", "2075246", "359870", "76579", "7844", "61424", "55065", "61434", "2016279", "71877", "2271483", "305269", "57405", "1842679" ]
[ "nonn" ]
43
0
1
[ "A000319", "A381230", "A381231" ]
null
N. J. A. Sloane, Feb 28 2025
2025-03-14T02:33:30
oeisdata/seq/A381/A381231.seq
2603b2eb6840b77eacaf8d26d17aaf66
A381232
Count down from k to -k for k = 0, 1, 2, ... .
[ "0", "1", "0", "-1", "2", "1", "0", "-1", "-2", "3", "2", "1", "0", "-1", "-2", "-3", "4", "3", "2", "1", "0", "-1", "-2", "-3", "-4", "5", "4", "3", "2", "1", "0", "-1", "-2", "-3", "-4", "-5", "6", "5", "4", "3", "2", "1", "0", "-1", "-2", "-3", "-4", "-5", "-6", "7", "6", "5", "4", "3", "2", "1", "0", "-1", "-2", "-3", "-4", "-5", "-6", "-7", "8", "7", "6", "5", "4", "3", "2", "1", "0", "-1", "-2", "-3", "-4", "-5", "-6", "-7", "-8", "9", "8", "7", "6", "5", "4", "3", "2", "1", "0", "-1", "-2", "-3", "-4", "-5", "-6", "-7", "-8", "-9" ]
[ "sign", "easy" ]
18
0
5
[ "A196199", "A381232", "A381233" ]
null
N. J. A. Sloane, Mar 01 2025 [Suggested by Franklin T. Adams-Watters, Sep 21 2011]
2025-03-02T08:01:42
oeisdata/seq/A381/A381232.seq
d6b186820286e7859a4863e3e98fb235
A381233
Concatenate the sequences S(k) = [0, 1, -1, ..., k, -k] for k = 0, 1, ...
[ "0", "0", "1", "-1", "0", "1", "-1", "2", "-2", "0", "1", "-1", "2", "-2", "3", "-3", "0", "1", "-1", "2", "-2", "3", "-3", "4", "-4", "0", "1", "-1", "2", "-2", "3", "-3", "4", "-4", "5", "-5", "0", "1", "-1", "2", "-2", "3", "-3", "4", "-4", "5", "-5", "6", "-6", "0", "1", "-1", "2", "-2", "3", "-3", "4", "-4", "5", "-5", "6", "-6", "7", "-7", "0", "1", "-1", "2", "-2", "3", "-3", "4", "-4", "5", "-5", "6", "-6", "7", "-7", "8", "-8", "0", "1", "-1", "2", "-2", "3", "-3", "4", "-4", "5", "-5", "6", "-6", "7", "-7", "8", "-8", "9", "-9" ]
[ "sign", "easy" ]
10
0
8
[ "A196199", "A381232", "A381233" ]
null
N. J. A. Sloane, Mar 01 2025 [Suggested by Franklin T. Adams-Watters, Sep 21 2011]
2025-03-01T16:45:27
oeisdata/seq/A381/A381233.seq
e88dad67a177e35968a33a1e23ad301e
A381234
RUNS transform of A000319.
[ "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "4", "1", "1", "2", "1", "1", "1", "1", "7", "1", "1", "2", "1", "1", "2", "1", "2", "1", "8", "1", "1", "1", "1", "18", "1", "1", "1", "1", "1", "1", "1", "1", "1", "825", "2", "1", "2", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "1", "2", "1", "1", "76", "1", "1", "1", "1", "2", "1", "1", "3", "2", "1", "1", "1", "1", "1", "1", "29", "1", "1", "1", "1", "2", "1", "1", "2", "1", "1", "1144", "1", "1", "188", "1", "1", "4571", "1", "1", "62" ]
[ "nonn" ]
18
1
1
[ "A000319", "A381234", "A381235" ]
null
N. J. A. Sloane, Mar 16 2025
2025-03-18T07:21:19
oeisdata/seq/A381/A381234.seq
3d72ab63cda51858674e7a20b9aeb9ca
A381235
a(n) = the term of A000319 that is repeated in the n-th run of equal consecutive terms.
[ "1", "74", "-1", "-2", "-3", "0", "1", "30", "-2", "29", "1", "4", "-6", "0", "1", "2", "-1", "-2", "-9", "0", "1", "2", "-2", "-35", "-1", "-2", "-3", "0", "1", "5", "-2", "3", "1", "-4", "-1", "-2", "-3", "1", "2", "-1", "-2", "-3", "0", "1", "2", "-1", "-2", "-21", "-7", "0", "1", "-4", "-1", "-2", "7", "2", "-3", "1", "-8", "-3", "1", "-3", "1", "3", "0", "1", "-22", "0", "1", "6", "-1", "-2", "-3", "1", "6", "0", "1", "2", "-1", "-2", "5", "-3", "1", "42", "-2", "2", "-1", "-2", "-3", "1", "-11", "-1", "-2", "-4", "-1" ]
[ "sign" ]
9
1
2
[ "A000319", "A381234", "A381235" ]
null
N. J. A. Sloane, Mar 16 2025.
2025-03-16T22:55:56
oeisdata/seq/A381/A381235.seq
0482687bbc69925a2e541b91b0d1984b
A381236
Irregular triangle read by rows: to get row n, take all the numbers that can be obtained by permuting the digits of 9*n, divide them by 9, and arrange them in order.
[ "0", "1", "2", "9", "3", "8", "4", "7", "5", "6", "5", "6", "4", "7", "3", "8", "2", "9", "1", "10", "11", "2", "9", "12", "20", "89", "90", "13", "19", "79", "14", "18", "24", "29", "68", "69", "15", "17", "35", "39", "57", "59", "16", "46", "49", "15", "17", "35", "39", "57", "59", "14", "18", "24", "29", "68", "69", "13", "19", "79", "2", "9", "12", "20", "89", "90", "21", "22", "91", "99", "102", "109" ]
[ "nonn", "tabf", "base" ]
18
0
3
[ "A381236", "A381237" ]
null
N. J. A. Sloane, Mar 16 2025
2025-03-17T15:39:31
oeisdata/seq/A381/A381236.seq
66d4f50190887c06539dc0eb79d834ca
A381237
a(n) = sum of row n of A381236.
[ "0", "1", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "222", "111", "222", "222", "111", "222", "222", "111", "222", "444", "444", "222", "222", "111", "222", "222", "111", "222", "222", "444", "222", "444", "222", "222", "222", "37", "222", "222", "222", "444", "444", "444", "444", "222", "111", "222", "222", "111", "222", "444", "444", "222", "444" ]
[ "nonn", "base" ]
14
0
3
[ "A381236", "A381237" ]
null
N. J. A. Sloane, Mar 16 2025
2025-03-17T15:33:22
oeisdata/seq/A381/A381237.seq
bf5ae29b60d3800a969157417473bd73
A381238
a(n) = floor(b(n)), where b(n) = sec^2(b(n-1)), b(0)=1.
[ "1", "3", "1", "4", "66", "1", "11", "4", "8", "3", "1", "6", "1", "143", "2", "1", "481", "10", "14", "6", "1", "4", "11", "2", "1", "140", "3", "1", "3", "1", "7", "14", "2", "2", "1", "3", "1", "39", "3", "1", "2159", "3", "1", "4", "3", "1", "3", "1", "14", "10", "1", "11", "6", "1", "3", "1", "4", "185", "1", "3", "1", "4", "78", "1", "3", "1", "6", "1", "4", "3", "2", "2", "1", "11", "17", "8", "15", "1", "16", "5", "1", "14", "4", "8", "7", "1", "20", "7", "96", "14", "62", "1", "3", "2", "2", "1", "91", "1", "10", "97", "1" ]
[ "nonn" ]
17
0
2
[ "A000319", "A005699", "A381238", "A382148" ]
null
N. J. A. Sloane, Mar 17 2025
2025-03-18T12:57:09
oeisdata/seq/A381/A381238.seq
975913ff87d1be07370231c4171f7783
A381239
Primes of the form Sum_{k >= 0} floor(m/5^k) for some number m.
[ "2", "3", "7", "13", "19", "31", "37", "41", "43", "47", "53", "59", "71", "83", "89", "97", "101", "103", "107", "109", "113", "127", "131", "137", "139", "149", "151", "157", "163", "181", "191", "193", "197", "199", "211", "227", "233", "239", "251", "257", "263", "269", "271", "277", "281", "283", "293", "307", "313", "331", "337", "347", "349", "353", "359" ]
[ "nonn" ]
4
1
1
[ "A191610", "A380662", "A381239" ]
null
Clark Kimberling, Mar 09 2025
2025-03-16T18:24:17
oeisdata/seq/A381/A381239.seq
82a57349db1fc4d0f6b0b1c330aa3036
A381240
Indices of records in A381096.
[ "1", "6", "10", "12", "14", "18", "22", "24", "28", "30", "42", "54", "60", "66", "78", "84", "90", "102", "114", "120", "126", "132", "138", "150", "168", "180", "198", "204", "210", "240", "252", "264", "270", "294", "300", "330", "360", "378", "390", "420", "450", "462", "480", "504", "510", "540", "546", "570", "600", "630", "660", "690", "714", "750", "780", "810", "840" ]
[ "nonn" ]
8
1
2
[ "A000010", "A005361", "A024619", "A381096", "A381240", "A381241" ]
null
Michael De Vlieger, Feb 18 2025
2025-02-25T11:41:00
oeisdata/seq/A381/A381240.seq
0b64b0a82d825cf2e4efd5aeea3276b7
A381241
Records in A381096.
[ "0", "3", "5", "6", "7", "10", "11", "13", "14", "21", "29", "33", "42", "45", "53", "58", "64", "69", "77", "85", "88", "90", "93", "108", "117", "128", "136", "138", "161", "172", "176", "181", "195", "208", "216", "249", "258", "267", "293", "322", "326", "341", "347", "354", "381", "390", "401", "425", "434", "484", "498", "513", "521", "547", "586", "590", "645", "652" ]
[ "nonn" ]
5
1
2
[ "A381096", "A381240", "A381241" ]
null
Michael De Vlieger, Feb 24 2025
2025-02-25T11:41:14
oeisdata/seq/A381/A381241.seq
0d93c8cb1f4c9815a6a19db090801d17
A381242
Lexicographically earliest sequence of distinct terms > 1 such that no term is a substring of the product of any two terms.
[ "2", "3", "20", "22", "28", "30", "200", "202", "220", "248", "280", "300", "2000", "2002", "2020", "2022", "2200", "2480", "2800", "3000", "3252", "3272", "20000", "20002", "20020", "20022", "20200", "20220", "22000", "23252", "24800", "28000", "30000", "32520", "32720", "200000", "200002", "200020", "200022", "200200", "200202", "200220" ]
[ "nonn", "base" ]
16
1
1
[ "A381242", "A382453" ]
null
Dominic McCarty, Mar 24 2025
2025-03-26T21:47:33
oeisdata/seq/A381/A381242.seq
aee616f64e965c022889e1ffc49d7bda
A381243
Number of hyperplanes defined by the nonzero differences of two permutations of order n.
[ "0", "0", "1", "6", "85", "1370", "30481", "778610", "24409645", "881325366", "36635553601", "1713454403210", "89415912126223", "5143372266050837", "323667807885619744", "22112062644980805684" ]
[ "nonn", "more" ]
10
0
4
[ "A019589", "A175176", "A362968", "A381243", "A381244", "A381339" ]
null
Max Alekseyev, Feb 17 2025
2025-02-24T04:17:57
oeisdata/seq/A381/A381243.seq
0faee9a63adc26046de351f162abecbd
A381244
Number of regions in the arrangement of hyperplanes corresponding to the nonzero differences of two permutations of order n.
[ "1", "1", "2", "12", "3696" ]
[ "nonn", "more", "hard" ]
9
0
3
[ "A019589", "A175176", "A362968", "A381243", "A381244" ]
null
Max Alekseyev, Feb 17 2025
2025-02-18T19:00:05
oeisdata/seq/A381/A381244.seq
e63ce8bcc3d5adf48c19ae44ccfb8a27
A381245
Numbers that are partial sums of the reverses of the sequence of primes and are reverses of primes.
[ "2", "5", "17", "358", "775", "3145", "7813", "10277", "13978", "15232", "19478", "32324", "36056", "70042", "71396", "72893", "76856", "102374", "141982", "155585", "301291", "331357", "332588", "354643", "717817", "763586", "791641", "799532", "922981", "931705", "935117", "940241", "952975", "993551", "1020461", "1028383", "1060075", "1094099", "1126831", "1145257" ]
[ "nonn", "base" ]
8
1
1
[ "A004087", "A071602", "A381245" ]
null
Robert Israel, Feb 17 2025
2025-02-18T18:50:39
oeisdata/seq/A381/A381245.seq
f99151e61ef3452e65e48348bb8fd0ce
A381247
Positive integers m such that m * (m+1) contains at least 8 decimal digits that are in neither m nor m+1.
[ "77776", "88888", "444554", "554544", "655555", "656565", "656665", "888787", "888888", "1111121", "1212121", "1222121", "2212121", "2222232", "2222332", "2223222", "2232222", "2322322", "2332222", "3223232", "3223332", "3232222", "3233322", "3322332", "3323232", "3443443", "4334443", "4343443", "4444443", "4544444", "5444444", "5445554", "5455454" ]
[ "nonn", "base" ]
25
1
1
[ "A381247", "A381248" ]
null
Ali Sada and M. F. Hasler, Feb 17 2025
2025-02-19T10:21:00
oeisdata/seq/A381/A381247.seq
12c76e64b431b54f1d3a1c10c59d1429
A381248
a(n) = least positive integer m such that m*(m+1) has n-2 distinct digits in base n, all distinct from those (base-n digits) of m and m+1.
[ "1", "4", "14", "156", "20", "750", "1763", "22142", "77776", "64420", "2443077", "52663933", "227623468", "1097568095", "3149642939", "81965144711", "105625962315", "143416754568", "8084207326294", "2574579252942508", "14079288482520493", "68732231173154643", "33344665050312525", "350798169613138819009", "201175550741393337488" ]
[ "nonn", "base" ]
33
2
2
[ "A381247", "A381248" ]
null
Ali Sada and M. F. Hasler, Feb 17 2025
2025-02-18T22:42:49
oeisdata/seq/A381/A381248.seq
c9f370c52a61db371e023408c915a0a1
A381249
Indices of records in k/A001414(k), k>=2.
[ "2", "6", "8", "9", "12", "15", "16", "18", "24", "27", "32", "36", "40", "45", "48", "54", "60", "64", "72", "80", "81", "90", "96", "108", "120", "128", "135", "144", "160", "162", "180", "192", "216", "240", "243", "270", "288", "320", "324", "360", "384", "405", "432", "480", "486", "540", "576", "640", "648", "720", "729", "810", "864", "960", "972", "1024", "1080", "1152" ]
[ "nonn", "new" ]
14
1
1
[ "A001414", "A082299", "A082343", "A082344", "A381249", "A381972" ]
null
Clark Kimberling, Apr 19 2025
2025-04-27T14:54:02
oeisdata/seq/A381/A381249.seq
6548474b275b868fa421f59fc104b035
A381251
a(n) is the number of ways to write prime(n) as a sum of distinct composites.
[ "0", "0", "0", "0", "0", "1", "1", "3", "4", "10", "14", "27", "40", "52", "74", "133", "229", "276", "457", "626", "744", "1189", "1599", "2498", "4450", "5862", "6752", "8835", "10139", "13189", "32481", "41614", "60099", "67900", "122825", "138101", "195147", "274193", "342783", "477381", "661502", "736865", "1252245", "1390615", "1711496", "1897886" ]
[ "nonn", "new" ]
23
1
8
[ "A000040", "A002808", "A053872", "A071904", "A204389", "A381251", "A383037" ]
null
Felix Huber, Apr 19 2025
2025-04-24T13:23:57
oeisdata/seq/A381/A381251.seq
d3903df6dd1d8b91bdfc7e7abb30230f
A381252
Decimal expansion of the area of the biggest little octagon.
[ "7", "2", "6", "8", "6", "8", "4", "8", "2", "7", "5", "1", "6", "2", "6", "7", "6", "6", "8", "3", "8", "1", "8", "6", "5", "3", "8", "1", "0", "3", "5", "5", "9", "2", "0", "3", "7", "5", "1", "7", "2", "2", "1", "2", "1", "6", "0", "8", "8", "3", "8", "5", "4", "0", "6", "4", "9", "9", "3", "8", "9", "0", "5", "6", "4", "7", "6", "1", "5", "0", "0", "6", "8", "3", "3", "7", "8", "6", "2", "3", "3", "3", "4", "0", "2", "8", "3", "0", "8", "7", "9", "1", "6", "1", "5", "0", "4", "6", "8", "5", "3", "9", "5", "0", "9", "8", "8", "2", "4", "5", "2", "4", "3", "5", "7", "8", "6", "6", "7", "5" ]
[ "nonn", "cons", "new" ]
12
1
1
[ "A111969", "A381252", "A383173" ]
null
Eric W. Weisstein, Apr 17 2025
2025-04-20T08:40:28
oeisdata/seq/A381/A381252.seq
f9c5c69c433300023bca0b9d8c9599a0
A381255
Positive integers not of the form round(2^(k+2)/5). Complement of A007910.
[ "4", "5", "7", "8", "9", "10", "11", "12", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49", "50", "52", "53", "54", "55", "56", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66", "67", "68", "69", "70", "71", "72", "73", "74" ]
[ "nonn", "new" ]
12
1
1
[ "A007910", "A381255" ]
null
Chai Wah Wu, Apr 21 2025
2025-04-22T02:39:14
oeisdata/seq/A381/A381255.seq
f18116f31c862bb844614cb4f75269b1
A381256
Numbers k such that 5*k+1 divides 5^k+1.
[ "0", "1", "625", "57057", "7748433", "30850281", "111494625", "393423745", "499088601", "519341361", "1051107705", "1329416385", "1616038425", "2215448001", "2433936225", "2852972265", "3399207273", "4344683849", "4961725281", "5454760185", "5485530369", "6578054145", "6678031745", "7701979761", "7807302825" ]
[ "nonn" ]
12
1
3
[ "A222948", "A224486", "A230076", "A381256", "A381257", "A381258" ]
null
René-Louis Clerc, Feb 18 2025
2025-03-08T20:22:57
oeisdata/seq/A381/A381256.seq
91f11073d91cd2bab5ecbfeee0da6d7f
A381257
Numbers k such that 6*k+1 divides 6^k+1.
[ "0", "1", "6", "30", "58", "70", "73", "90", "101", "105", "121", "125", "146", "153", "166", "170", "181", "182", "185", "210", "233", "241", "242", "266", "282", "290", "322", "373", "381", "385", "390", "397", "441", "445", "446", "450", "453", "530", "557", "562", "585", "593", "601", "602", "605", "606", "621", "646", "653", "670", "685", "710", "726", "805", "810", "817", "833", "837", "853", "866" ]
[ "nonn" ]
16
1
3
[ "A222948", "A224486", "A230076", "A381256", "A381257", "A381258" ]
null
René-Louis Clerc, Feb 18 2025
2025-04-02T20:58:20
oeisdata/seq/A381/A381257.seq
ec028debef683e2646f562de1ed9eb4f
A381258
Numbers k such that 7*k+1 divides 7^k+1.
[ "0", "1", "135", "5733", "11229", "42705", "50445", "117649", "131365", "168093", "636405", "699825", "1269495", "2528155", "4226175", "6176709", "6502545", "9365265", "9551115", "13227021", "14464485", "14912625", "20859435", "26903605", "28251265", "30589905", "32660901", "37597329", "41506875", "42766465", "55452075", "56192535", "111898605" ]
[ "nonn" ]
20
1
3
[ "A222948", "A224486", "A230076", "A381256", "A381257", "A381258" ]
null
René-Louis Clerc, Feb 18 2025
2025-03-05T12:06:33
oeisdata/seq/A381/A381258.seq
c762b8d87894333dc6778bbcc4645579
A381259
Numbers obtained by concatenating powers of 2, sorted into increasing order.
[ "1", "2", "4", "8", "11", "12", "14", "16", "18", "21", "22", "24", "28", "32", "41", "42", "44", "48", "64", "81", "82", "84", "88", "111", "112", "114", "116", "118", "121", "122", "124", "128", "132", "141", "142", "144", "148", "161", "162", "164", "168", "181", "182", "184", "188", "211", "212", "214", "216", "218", "221", "222", "224", "228", "232", "241", "242", "244", "248", "256", "264" ]
[ "nonn", "base", "easy" ]
22
1
2
[ "A000079", "A028846", "A045507", "A152242", "A178664", "A381259" ]
null
Stefano Spezia, Feb 18 2025
2025-02-20T12:58:18
oeisdata/seq/A381/A381259.seq
5787ab8d622f4415740d446eb45a467f
A381260
Expansion of e.g.f. exp( -LambertW(-2 * x * cosh(x)) / 2 ).
[ "1", "1", "5", "52", "789", "16116", "415633", "12963952", "474761577", "19974663568", "949570545501", "50341473508800", "2944936306028797", "188445333393978688", "13094108333345047401", "981850811606401705216", "79025876659261666454481", "6795576727642475440025856", "621789675800920271144983477" ]
[ "nonn" ]
8
0
3
[ "A185951", "A381140", "A381260" ]
null
Seiichi Manyama, Feb 18 2025
2025-02-18T08:57:17
oeisdata/seq/A381/A381260.seq
ddbc71fab7791dea69a0c1601a2bb967
A381261
Expansion of e.g.f. exp( -LambertW(-2 * x * cos(x)) / 2 ).
[ "1", "1", "5", "46", "669", "13176", "328153", "9889328", "349998169", "14232282112", "653960139021", "33511444515968", "1894938691013173", "117209395966704640", "7872535432641217185", "570622024676568564736", "44395462114163659522353", "3690312836780077587120128", "326399124496126009678138261" ]
[ "nonn" ]
9
0
3
[ "A185951", "A381141", "A381261" ]
null
Seiichi Manyama, Feb 18 2025
2025-02-18T08:57:22
oeisdata/seq/A381/A381261.seq
08d903cac2e79ff2d03fc5ddc934cdc3
A381262
Expansion of e.g.f. exp( -LambertW(-2 * sinh(x)) / 2 ).
[ "1", "1", "5", "50", "749", "15132", "385953", "11907520", "431376345", "17954558928", "844397935517", "44287052219104", "2563077440429701", "162259043437047104", "11154216390820950585", "827464985582299977728", "65889383717510410496689", "5605511011776107945980160", "507429545895353798767136181" ]
[ "nonn" ]
9
0
3
[ "A136630", "A219503", "A381262" ]
null
Seiichi Manyama, Feb 18 2025
2025-02-18T08:57:27
oeisdata/seq/A381/A381262.seq
d8c02d1a1ef7fc2bd438f76acc328ef2
A381263
Expansion of e.g.f. exp( -LambertW(-2 * sin(x)) / 2 ).
[ "1", "1", "5", "48", "709", "14152", "356793", "10882648", "389790889", "16040853568", "745908722477", "38681745244032", "2213527304014189", "138556837227204736", "9417928265797994145", "690818806495197538816", "54391227913053881634001", "4575388875753714015748096", "409532433006878699321370197" ]
[ "nonn" ]
8
0
3
[ "A136630", "A381142", "A381263" ]
null
Seiichi Manyama, Feb 18 2025
2025-02-18T08:57:33
oeisdata/seq/A381/A381263.seq
7c5e6e8f41bda079bdf18e68943a1025
A381264
Decimal expansion of the edge length of the dodecahedron inside a circumscribed unit sphere.
[ "7", "1", "3", "6", "4", "4", "1", "7", "9", "5", "4", "6", "1", "7", "9", "8", "6", "3", "8", "8", "3", "9", "3", "9", "6", "8", "6", "0", "9", "2", "1", "7", "5", "7", "4", "7", "9", "6", "3", "3", "7", "2", "1", "5", "0", "4", "9", "3", "7", "3", "6", "7", "3", "2", "8", "4", "3", "9", "2", "2", "2", "6", "2", "2", "2", "0", "5", "1", "6", "6", "9", "1", "6", "7", "6", "0", "5", "9", "6", "6", "5", "4", "7", "9", "3", "8", "0", "3", "9", "6", "7", "0" ]
[ "nonn", "cons" ]
21
0
1
[ "A001622", "A156547", "A179296", "A381264" ]
null
R. J. Mathar, Feb 18 2025
2025-02-26T02:13:08
oeisdata/seq/A381/A381264.seq
93e638349aada9f6db6634f4edd516e7
A381265
a(n) is the number of solid (3D) partitions of n with 2 layers and second layer a plane partition of 3.
[ "6", "21", "57", "138", "294", "606", "1170", "2208", "4008", "7176", "12492", "21510", "36348", "60801", "100281", "164019", "265263", "425853" ]
[ "nonn", "more" ]
8
3
1
[ "A000041", "A000219", "A000990", "A378854", "A381265" ]
null
Wouter Meeussen, Feb 18 2025
2025-02-18T19:00:44
oeisdata/seq/A381/A381265.seq
cafb92d5b02784f7d987931a425cfb99
A381266
a(n) = least positive integer m such that when m*(m+1) is written in base n, it contains every single digit exactly once, or 0 if no such number exists.
[ "1", "0", "12", "34", "134", "0", "1477", "6891", "38627", "0", "891230", "4874690", "28507439", "0", "1078575795", "7002987575", "46916000817", "0", "2295911609450", "16720559375850", "124852897365573", "0", "7468470450367652", "59705969514613035", "487357094495846175", "0", "34452261762372201726", "297930994005481958694" ]
[ "nonn", "base" ]
27
2
3
[ "A381248", "A381266" ]
null
Daniel Mondot and Ali Sada, Feb 18 2025
2025-03-17T22:15:51
oeisdata/seq/A381/A381266.seq
f7bb48d2c0ef65b233942ff428391f69
A381267
a(n) = numerator( [(x*y*z*u)^n] 1/sqrt(1 - (x + y + z + u*(y + z))) ).
[ "1", "15", "31185", "6381375", "409933148625", "115551955934415", "561860686475913825", "179982394552964750175", "245527483089290688069980625", "84259935283701238220954169375", "473788223464393905637179153328785", "169752647693877043154936308907932575", "15821279983229628402902553309640505635425" ]
[ "nonn", "frac" ]
10
0
2
[ "A009971", "A134375", "A381267", "A381268" ]
null
Stefano Spezia, Feb 18 2025
2025-02-19T13:37:44
oeisdata/seq/A381/A381267.seq
390b466c384f53d9d71cbf58745968f3
A381268
a(n) = denominator( [(x*y*z*u)^n] 1/sqrt(1 - (x + y + z + u*(y + z))) ).
[ "1", "4", "256", "1024", "1048576", "4194304", "268435456", "1073741824", "17592186044416", "70368744177664", "4503599627370496", "18014398509481984", "18446744073709551616", "73786976294838206464", "4722366482869645213696", "18889465931478580854784", "4951760157141521099596496896", "19807040628566084398385987584" ]
[ "nonn", "frac" ]
8
0
2
[ "A009971", "A134375", "A278142", "A381267", "A381268" ]
null
Stefano Spezia, Feb 18 2025
2025-02-19T13:37:32
oeisdata/seq/A381/A381268.seq
94ba485fea6be037829ecc2156014463
A381269
a(n) = numerator( [x*y*z]^n 1/sqrt((1 - (x + y + z))*(1 - y - z^2)) ).
[ "1", "9", "1695", "26215", "120986775", "9502702209", "789204625209", "34080236440965", "1551341154742525575", "141040042903795882275", "52208336916743049297255", "306352374268280009960745", "1862930539686953773794528225", "178800539000323387892726124675", "34618577499107880715911257143875" ]
[ "nonn", "frac" ]
10
0
2
[ "A381269", "A381270", "A381271", "A381272" ]
null
Stefano Spezia, Feb 18 2025
2025-02-19T13:37:24
oeisdata/seq/A381/A381269.seq
f3cc8e1583004be9e19f1bb92d431288
A381270
a(n) = denominator( [x*y*z]^n 1/sqrt((1 - (x + y + z))*(1 - y - z^2)) ).
[ "1", "4", "64", "64", "16384", "65536", "262144", "524288", "1073741824", "4294967296", "68719476736", "17179869184", "4398046511104", "17592186044416", "140737488355328", "281474976710656", "4611686018427387904", "18446744073709551616", "295147905179352825856", "295147905179352825856", "75557863725914323419136" ]
[ "nonn", "frac" ]
9
0
2
[ "A381269", "A381270", "A381271", "A381272" ]
null
Stefano Spezia, Feb 18 2025
2025-02-19T13:37:15
oeisdata/seq/A381/A381270.seq
74b540352b31b243d26d85d708fc3805
A381271
a(n) = numerator( [x*y*z]^n 1/sqrt((1 - (x + y + z))*(1 - x - y - z^2)) ).
[ "1", "3", "195", "665", "820575", "15306291", "321221901", "3400981155", "38681474812695", "872267067639825", "80552172130705275", "117735218601670215", "178666542358192113225", "4278458781930443466825", "206819443902585382527375", "2518237991059733983111695", "252890952855692468573188869255", "6236413379907980580174936458925", "618385442772270188414534006897025" ]
[ "nonn", "frac", "changed" ]
22
0
2
[ "A381269", "A381270", "A381271", "A381272" ]
null
Stefano Spezia, Feb 18 2025
2025-04-14T03:14:07
oeisdata/seq/A381/A381271.seq
00dea08b7f9e63d6fea58a18ccf05700
A381272
a(n) = denominator( [x*y*z]^n 1/sqrt((1 - (x + y + z))*(1 - x - y - z^2)) ).
[ "1", "1", "4", "1", "64", "64", "64", "32", "16384", "16384", "65536", "4096", "262144", "262144", "524288", "262144", "1073741824", "1073741824", "4294967296", "1073741824", "68719476736", "68719476736", "17179869184", "8589934592", "4398046511104", "4398046511104", "17592186044416", "2199023255552", "140737488355328", "140737488355328", "281474976710656", "140737488355328", "4611686018427387904" ]
[ "nonn", "frac", "changed" ]
23
0
3
[ "A381269", "A381270", "A381271", "A381272" ]
null
Stefano Spezia, Feb 18 2025
2025-04-14T03:15:02
oeisdata/seq/A381/A381272.seq
9eb8055f5a750cdfa6a2f58df641e088
A381273
Expansion of e.g.f. exp(x * cosh(2*x)).
[ "1", "1", "1", "13", "49", "201", "2161", "12629", "102817", "1118161", "9109921", "105660765", "1223720785", "13461561881", "186666204817", "2406325357861", "33607592404033", "516511765519521", "7658010172957249", "126206019752173997", "2115466479287184241", "36218229615683409001", "666810643855970901937" ]
[ "sign" ]
11
0
4
[ "A003727", "A185951", "A381273", "A381274" ]
null
Seiichi Manyama, Feb 18 2025
2025-02-19T03:40:32
oeisdata/seq/A381/A381273.seq
d7d288dbe4aace2cb7967612b4bf8982
A381274
Expansion of e.g.f. exp(x * cosh(3*x)).
[ "1", "1", "1", "28", "109", "676", "10261", "65584", "881497", "11930896", "122708521", "2186539840", "30542901445", "477545743936", "9168255077437", "149358238356736", "3043023842477233", "61000460650291456", "1225825910880514129", "28395625697194028032", "621110654837608378141", "14936817377079335166976" ]
[ "nonn" ]
9
0
4
[ "A003727", "A185951", "A381273", "A381274" ]
null
Seiichi Manyama, Feb 18 2025
2025-02-19T03:36:34
oeisdata/seq/A381/A381274.seq
b15238cfbc160c2fd4d6b7a4632b6d75
A381275
Expansion of e.g.f. exp(x * cos(2*x)).
[ "1", "1", "1", "-11", "-47", "-39", "1681", "10893", "-13215", "-851471", "-5515679", "34375397", "887687857", "3982645577", "-85350572943", "-1466457337859", "-659043831871", "270733024430305", "3181606182917569", "-24432689736388395", "-1076204061663657839", "-6834631528147762247", "221729710998069153617" ]
[ "sign" ]
9
0
4
[ "A009189", "A185951", "A381275", "A381276" ]
null
Seiichi Manyama, Feb 18 2025
2025-02-19T03:36:48
oeisdata/seq/A381/A381275.seq
f5877d929fb66560e6b413f82a7acf01
A381276
Expansion of e.g.f. exp(x * cos(3*x)).
[ "1", "1", "1", "-26", "-107", "136", "9181", "53488", "-427895", "-10486016", "-43859879", "1373548672", "23512856797", "-30564574208", "-6412871847563", "-73709639926784", "1060067525174929", "40587133606543360", "179320588932698929", "-14474677657838059520", "-306563699887974043739", "2301792469199499132928" ]
[ "sign" ]
12
0
4
[ "A009189", "A185951", "A352643", "A381275", "A381276", "A381283" ]
null
Seiichi Manyama, Feb 18 2025
2025-02-19T03:37:08
oeisdata/seq/A381/A381276.seq
f92720b6e47e3750d02dfd087c5b2010
A381277
Expansion of e.g.f. exp(sinh(3*x) / 3).
[ "1", "1", "1", "10", "37", "172", "1477", "8416", "74377", "683344", "5836969", "67102048", "699721453", "8268521536", "107106298093", "1347611617792", "19462095444241", "279380302430464", "4247519795325649", "68946703997616640", "1122787065355425973", "19697500164381137920", "351304020205694058133" ]
[ "nonn" ]
8
0
4
[ "A003724", "A009229", "A136630", "A381277" ]
null
Seiichi Manyama, Feb 18 2025
2025-02-19T03:37:22
oeisdata/seq/A381/A381277.seq
e50394064509b799518bde2f3518997a
A381278
Expansion of e.g.f. exp(sin(3*x) / 3).
[ "1", "1", "1", "-8", "-35", "-8", "1117", "6328", "-19943", "-513728", "-2096711", "30574720", "447401845", "23791744", "-59033858219", "-527680180736", "4971322421425", "144677554315264", "430091284739185", "-27641200139694080", "-398305237630617971", "2876369985206861824", "145441158283475935309" ]
[ "sign" ]
10
0
4
[ "A002017", "A009210", "A136630", "A352640", "A381278", "A381286" ]
null
Seiichi Manyama, Feb 18 2025
2025-02-19T03:37:37
oeisdata/seq/A381/A381278.seq
0277c5aef1bd8b2480bc69b4f3a24aee
A381279
a(1) = 1, for n > 1, a(n) = a(n - 1) / 2 if a(n - 1) is divisible by 2, otherwise a(n) = a(n - 1) + A000005(n - 1).
[ "1", "2", "1", "3", "6", "3", "7", "9", "13", "16", "8", "4", "2", "1", "5", "9", "14", "7", "13", "15", "21", "25", "29", "31", "39", "42", "21", "25", "31", "33", "41", "43", "49", "53", "57", "61", "70", "35", "39", "43", "51", "53", "61", "63", "69", "75", "79", "81", "91", "94", "47", "51", "57", "59", "67", "71", "79", "83", "87", "89", "101", "103", "107", "113", "120", "60", "30", "15", "21", "25" ]
[ "nonn" ]
22
1
2
[ "A000005", "A381279" ]
null
Ctibor O. Zizka, Apr 12 2025
2025-04-13T16:17:47
oeisdata/seq/A381/A381279.seq
297ad08f2458e5af1e4a96ade7701491
A381280
Expansion of e.g.f. 1/(1 - x * cosh(2*x)).
[ "1", "1", "2", "18", "120", "920", "10320", "126448", "1714048", "27073152", "472354560", "8989147904", "187690331136", "4245706716160", "103239264593920", "2691918892861440", "74885151106498560", "2212607133043884032", "69227613551324233728", "2286465386258267176960", "79487593489348266557440" ]
[ "nonn", "changed" ]
12
0
3
[ "A185951", "A201939", "A205571", "A381280", "A381281" ]
null
Seiichi Manyama, Feb 18 2025
2025-04-19T07:16:15
oeisdata/seq/A381/A381280.seq
f47950ad5b45682c74a4cb4d83f44911
A381281
Expansion of e.g.f. 1/(1 - x * cosh(3*x)).
[ "1", "1", "2", "33", "240", "2145", "33120", "480753", "7878528", "158696577", "3384322560", "78934776129", "2053186983936", "57231998680545", "1714372871178240", "55323775198258065", "1899762412262031360", "69264871449203672577", "2677542944055160209408", "109197154520146527569505" ]
[ "nonn" ]
8
0
3
[ "A185951", "A205571", "A381280", "A381281" ]
null
Seiichi Manyama, Feb 18 2025
2025-02-19T03:38:05
oeisdata/seq/A381/A381281.seq
c3d19c287a55fdfa384e1e4bb1e64c41
A381282
Expansion of e.g.f. 1/(1 - x * cos(2*x)).
[ "1", "1", "2", "-6", "-72", "-520", "-1200", "24752", "516992", "5106816", "5287680", "-998945024", "-23719719936", "-272471972864", "1326261594112", "149170761246720", "3843177252618240", "42752553478356992", "-863092250325614592", "-59317347865870139392", "-1577115871098630307840", "-13173264127625587851264" ]
[ "sign" ]
10
0
3
[ "A185951", "A352252", "A381282", "A381283" ]
null
Seiichi Manyama, Feb 18 2025
2025-02-19T03:38:20
oeisdata/seq/A381/A381282.seq
68418cb99d80cf3ef4299707e24179ad
A381283
Expansion of e.g.f. 1/(1 - x * cos(3*x)).
[ "1", "1", "2", "-21", "-192", "-1095", "7200", "243747", "3088512", "1360881", "-874437120", "-21701765349", "-186175604736", "5870711879721", "292185085151232", "5507319584787795", "-38951106749890560", "-6402114772676575263", "-212680600451474522112", "-1602903494245708491957", "197042528380347210792960" ]
[ "sign" ]
11
0
3
[ "A185951", "A352252", "A381282", "A381283" ]
null
Seiichi Manyama, Feb 18 2025
2025-02-19T03:38:33
oeisdata/seq/A381/A381283.seq
56cfe0b066a67d9262f5e4e761d2437e
A381284
Expansion of e.g.f. 1/(1 - sinh(3*x) / 3).
[ "1", "1", "2", "15", "96", "741", "7632", "87795", "1149696", "17155881", "282880512", "5128464375", "101592631296", "2178698451021", "50314379323392", "1245198047833755", "32868161979088896", "921803465256094161", "27373850876851126272", "858044392807801699935", "28311289100161039466496" ]
[ "nonn", "changed" ]
10
0
3
[ "A006154", "A136630", "A191277", "A381284" ]
null
Seiichi Manyama, Feb 18 2025
2025-04-19T06:00:02
oeisdata/seq/A381/A381284.seq
9d740fa8941fb2fd27462015ce2b839e
A381285
Expansion of e.g.f. 1/(1 - sin(2*x) / 2).
[ "1", "1", "2", "2", "-8", "-104", "-688", "-3088", "-128", "209536", "3145472", "29795072", "139389952", "-1715047424", "-60056147968", "-1004215072768", "-10305404960768", "-1945682345984", "2949643589844992", "84438462955323392", "1458284922371571712", "12032890515685113856", "-245515800089314459648" ]
[ "sign" ]
9
0
3
[ "A000111", "A136630", "A381285", "A381286" ]
null
Seiichi Manyama, Feb 18 2025
2025-02-19T03:38:57
oeisdata/seq/A381/A381285.seq
55b3275dea7330166c4d83d2b3ae589c
A381286
Expansion of e.g.f. 1/(1 - sin(3*x) / 3).
[ "1", "1", "2", "-3", "-48", "-339", "-1008", "10737", "237312", "2362041", "5432832", "-318158523", "-7615254528", "-87216236379", "173049219072", "33959321252217", "851545449234432", "9561733579228401", "-129701862228492288", "-9445723672920941043", "-239815723596207095808", "-2109465061216228379619" ]
[ "sign" ]
12
0
3
[ "A000111", "A136630", "A352638", "A381278", "A381285", "A381286" ]
null
Seiichi Manyama, Feb 18 2025
2025-02-19T03:39:09
oeisdata/seq/A381/A381286.seq
b524b96948384be5f38584c754db3e32
A381287
a(n) is the smallest nonnegative number congruent to k modulo prime(k)^(n-k+1) for k=1..n.
[ "1", "5", "353", "65153", "119966753", "3050486978753", "563678198162618753", "15413934869729743026218753", "1710386933322832904060816574218753", "14712401204424400291787297607394206774218753", "5027982881016562571248237683551040219315980699574218753", "5488604004979149030407333271782173318791620565366546226763574218753" ]
[ "nonn" ]
34
1
2
[ "A005687", "A006939", "A381287" ]
null
Steven Lu, Feb 19 2025
2025-03-15T04:23:18
oeisdata/seq/A381/A381287.seq
7970c3616ff48711544bc2ffc4bf69ee
A381288
Partial alternating sums of the trajectory of 2 under the morphism 2->{2,1,2}, 1->{2}.
[ "0", "2", "1", "3", "1", "3", "2", "4", "2", "3", "1", "3", "2", "4", "2", "4", "3", "5", "3", "4", "2", "4", "2", "3", "1", "3", "2", "4", "2", "4", "3", "5", "3", "4", "2", "4", "3", "5", "3", "5", "4", "6", "4", "5", "3", "5", "3", "4", "2", "4", "3", "5", "3", "4", "2", "4", "2", "3", "1", "3", "2", "4", "2", "4", "3", "5", "3", "4", "2", "4", "3", "5", "3", "5", "4", "6", "4", "5", "3", "5", "3", "4", "2", "4", "3", "5", "3" ]
[ "nonn", "easy" ]
44
0
2
[ "A001333", "A104521", "A106035", "A381288" ]
null
Keith J. Bauer, Apr 01 2025
2025-04-02T15:09:52
oeisdata/seq/A381/A381288.seq
a88ee451e7ac7468d0271721b50f923a
A381289
Number of subsets of 6 integers between 1 and n such that their sum is 0 modulo n.
[ "1", "3", "10", "20", "42", "76", "132", "212", "335", "497", "728", "1028", "1428", "1932", "2586", "3384", "4389", "5601", "7084", "8844", "10966", "13442", "16380", "19780", "23751", "28301", "33566", "39536", "46376", "54086", "62832", "72624", "83661", "95931", "109668", "124872", "141778", "160398", "181006" ]
[ "nonn", "easy" ]
35
7
2
[ "A011796", "A381289" ]
null
Xavier Roulleau and David Broadhurst, Feb 19 2025
2025-02-28T07:45:37
oeisdata/seq/A381/A381289.seq
3b9953e072ca0dd9cf62ae49acebb3f5
A381290
Number of subsets of 6 integers between 1 and n such that their sum is 1 modulo n.
[ "1", "4", "9", "22", "42", "78", "132", "217", "333", "504", "728", "1035", "1428", "1944", "2583", "3399", "4389", "5616", "7084", "8866", "10962", "13468", "16380", "19806", "23751", "28336", "33561", "39576", "46376", "54126", "62832", "72675", "83655", "95988", "109668", "124929", "141778", "160468", "180999" ]
[ "nonn", "easy" ]
22
7
2
[ "A011796", "A381289", "A381290" ]
null
Xavier Roulleau and David Broadhurst, Feb 19 2025
2025-02-28T07:45:46
oeisdata/seq/A381/A381290.seq
ed0a2622e99aa1755ae0efc72f6578ed
A381291
Number of subsets of 8 integers between 1 and n such that their sum is 0 modulo n.
[ "1", "5", "15", "43", "99", "217", "429", "809", "1430", "2438", "3978", "6310", "9690", "14550", "21318", "30666", "43263", "60115", "82225", "111041", "148005", "195143", "254475", "328755", "420732", "534076", "672452", "840652", "1043460", "1287036", "1577532", "1922740", "2330445", "2810385", "3372291", "4028183", "4790071" ]
[ "nonn" ]
22
9
2
[ "A011796", "A381289", "A381290", "A381291" ]
null
Xavier Roulleau and David Broadhurst, Feb 19 2025
2025-02-28T07:45:41
oeisdata/seq/A381/A381291.seq
1c71981d13bdf8bac2f049b71a14334f
A381292
Expansion of g.f. hypergeom([1/2, 3/4, 5/4], [1, 3/2], 256*x).
[ "1", "80", "12096", "2196480", "435635200", "91017658368", "19681596211200", "4361120388218880", "984138122900275200", "225245492144504832000", "52138539404512009912320", "12180522019129546663526400", "2867511425916768698757021696", "679455041354637369514813030400", "161892954188496214335204360192000" ]
[ "nonn" ]
8
0
2
[ "A001044", "A277757", "A381292" ]
null
Stefano Spezia, Feb 19 2025
2025-02-19T16:12:50
oeisdata/seq/A381/A381292.seq
9d19a36532e9de41bfac5ff4649343c7
A381293
a(n) is the least prime p such that the number of primes between p (not inclusive) and p+n*log(p) is n.
[ "11", "37", "37", "59", "59", "59", "79", "79", "71", "67", "67", "179", "137", "131", "127", "227", "223", "191", "347", "349", "349", "337", "331", "331", "347", "347", "347", "307", "557", "557", "431", "557", "557", "547", "541", "547", "541", "431", "811", "797", "569", "821", "809", "811", "797", "797", "797", "797", "797", "797" ]
[ "nonn" ]
8
1
1
null
null
Alain Rocchelli, Feb 19 2025
2025-03-05T19:02:20
oeisdata/seq/A381/A381293.seq
886ad5952996981da21ef6c060589d7f
A381294
Smallest number k such that there are n sets A_1,...,A_n with each A_i being a subset of {1,...,k} and the intersection of A_i and A_j has size |i-j| for all 1 <= i < j <= n.
[ "0", "0", "1", "2", "5", "9", "16", "24", "36", "50", "70", "91", "120", "150", "189", "231", "280", "336", "398", "468", "547", "630", "728" ]
[ "nonn", "more" ]
18
0
4
null
null
Jonas Seiler, Feb 19 2025
2025-03-06T14:42:06
oeisdata/seq/A381/A381294.seq
5a7f7da375241ca4135a6518e092bdbb
A381295
a(n) = numerator( [(x*y*z*u*v)^n] 1/sqrt(1 - (x + y + z + u + v*(x*y*z + x*y*u + x*z*u + y*z*u))) ).
[ "1", "3", "735", "1155", "152927775", "5729606883", "944642139441", "20804764619925", "31532612849128108575", "1514216480447305259625", "1198479499879816971151335", "15183210867901962855773895", "200941692389810767447918272225", "10564290945275296828332253777425", "4507504507128763568843859426010875" ]
[ "nonn", "frac" ]
8
0
2
[ "A381295", "A381296" ]
null
Stefano Spezia, Feb 19 2025
2025-02-20T08:37:36
oeisdata/seq/A381/A381295.seq
9215410b8174a050d84f4e27f2ff5c81
A381296
a(n) = denominator( [(x*y*z*u*v)^n] 1/sqrt(1 - (x + y + z + u + v*(x*y*z + x*y*u + x*z*u + y*z*u))) ).
[ "1", "1", "16", "1", "4096", "4096", "16384", "8192", "268435456", "268435456", "4294967296", "1073741824", "274877906944", "274877906944", "2199023255552", "1099511627776", "1152921504606846976", "1152921504606846976", "18446744073709551616", "2305843009213693952", "4722366482869645213696", "4722366482869645213696" ]
[ "nonn", "frac" ]
7
0
3
[ "A381295", "A381296" ]
null
Stefano Spezia, Feb 19 2025
2025-02-20T08:37:40
oeisdata/seq/A381/A381296.seq
9feacef023bd175c826dba02dbb58018
A381297
a(n) = numerator( [x^n] hypergeom([1/2, 1/2, 1/2, 1/4, 3/4], [1, 1, 1, 1], 256*x) ).
[ "1", "6", "2835", "144375", "9656521875", "727613515629", "1924950961452519", "169849119537100575", "515343459815505282121875", "49523686986654845229890625", "156852007784587147805477109405", "15901454576103641443903862431665", "1683931647757461343713885153275036775", "177089976268148398718338641838887890625" ]
[ "nonn", "frac" ]
9
0
2
[ "A381297", "A381298" ]
null
Stefano Spezia, Feb 19 2025
2025-02-20T08:37:44
oeisdata/seq/A381/A381297.seq
c5c0aa2de4f892bf777e66eaff5b501b
A381298
a(n) = denominator( [x^n] hypergeom([1/2, 1/2, 1/2, 1/4, 3/4], [1, 1, 1, 1], 256*x) ).
[ "1", "1", "8", "4", "2048", "1024", "16384", "8192", "134217728", "67108864", "1073741824", "536870912", "274877906944", "137438953472", "2199023255552", "1099511627776", "576460752303423488", "288230376151711744", "4611686018427387904", "2305843009213693952", "1180591620717411303424", "590295810358705651712", "9444732965739290427392" ]
[ "nonn", "frac" ]
7
0
3
[ "A381297", "A381298" ]
null
Stefano Spezia, Feb 19 2025
2025-02-20T08:37:48
oeisdata/seq/A381/A381298.seq
4e1cf7999d12297515344911df967785
A381299
Irregular triangular array read by rows. T(n,k) is the number of ordered set partitions of [n] with exactly k descents, n>=0, 0<=k<=binomial(n,2).
[ "1", "1", "2", "1", "4", "4", "4", "1", "8", "12", "18", "18", "12", "6", "1", "16", "32", "60", "84", "100", "92", "76", "48", "24", "8", "1", "32", "80", "176", "300", "448", "572", "650", "658", "596", "478", "334", "206", "102", "40", "10", "1", "64", "192", "480", "944", "1632", "2476", "3428", "4300", "5008", "5372", "5356", "4936", "4220", "3316", "2392", "1556", "904", "456", "188", "60", "12", "1" ]
[ "nonn", "tabf" ]
38
0
3
[ "A000670", "A001787", "A008302", "A011782", "A125810", "A161680", "A240796", "A268586", "A289545", "A347841", "A347842", "A347843", "A347844", "A347845", "A347846", "A381299" ]
null
Geoffrey Critzer, Feb 19 2025
2025-04-02T04:13:15
oeisdata/seq/A381/A381299.seq
1fca4c5248ebfb26732e30d28c718bbb
A381300
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cosh(x * A(x)^(1/2)) ).
[ "1", "1", "2", "9", "60", "485", "4800", "57547", "804160", "12783969", "228447360", "4539156941", "99244045824", "2367795157741", "61230675251200", "1706241143585175", "50971847057326080", "1625178125581055297", "55087299146009640960", "1978201530490562626609", "75025096312729021972480" ]
[ "nonn" ]
8
0
3
[ "A185951", "A381300" ]
null
Seiichi Manyama, Feb 19 2025
2025-02-20T08:39:24
oeisdata/seq/A381/A381300.seq
0dba0085ac9d79ffdeefd5f8dcd0b87a
A381301
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cos(x * A(x)^(1/2)) / A(x) ).
[ "1", "1", "0", "-3", "-12", "5", "240", "1463", "-2688", "-92223", "-662400", "3249169", "98672640", "733006573", "-7901816832", "-224782617165", "-1546734551040", "34327512843137", "929724626829312", "5081202564853445", "-243237724194078720", "-6276196972896490059", "-18788298569495347200", "2624677015793433809647" ]
[ "sign" ]
9
0
4
[ "A185951", "A381301" ]
null
Seiichi Manyama, Feb 19 2025
2025-02-20T08:39:28
oeisdata/seq/A381/A381301.seq
b280a811edeee1157df824b6026c1da3
A381302
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cos(x * A(x)^(1/2)) ).
[ "1", "1", "2", "3", "-12", "-235", "-2400", "-18067", "-51520", "1701009", "49829760", "872355319", "9861874176", "-8805084275", "-4518287900672", "-159719520182055", "-3608706518138880", "-44358720138978463", "748112236681789440", "72503399560668659531", "2875934090148742430720", "73418478070342765464741" ]
[ "sign" ]
9
0
3
[ "A185951", "A381302" ]
null
Seiichi Manyama, Feb 19 2025
2025-02-20T08:39:31
oeisdata/seq/A381/A381302.seq
7753f2f348400270d4b459b96253365d
A381303
E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)^(1/2)) / A(x)^(3/2) ).
[ "1", "1", "0", "1", "4", "1", "32", "183", "192", "4921", "33664", "88573", "2100224", "16487745", "83890176", "1920800731", "17243373568", "143156073841", "3236025171968", "33490813489497", "401094916964352", "9092346624868321", "109434837281013760", "1724106500663768191", "39706910863092875264" ]
[ "nonn" ]
7
0
5
[ "A136630", "A381303" ]
null
Seiichi Manyama, Feb 19 2025
2025-02-20T08:39:35
oeisdata/seq/A381/A381303.seq
675b4b753f2cefbec1fa58b77c81ff3b
A381304
E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)^(1/2)) / A(x)^(1/2) ).
[ "1", "1", "2", "7", "36", "241", "1984", "19461", "222080", "2892361", "42350976", "688911763", "12329035264", "240789209025", "5096898326528", "116247332597833", "2842225449025536", "74165478671163601", "2057366115038003200", "60461340544432547391", "1876511245926278365184", "61336532673286072390321" ]
[ "nonn" ]
7
0
3
[ "A136630", "A381304" ]
null
Seiichi Manyama, Feb 19 2025
2025-02-20T08:39:38
oeisdata/seq/A381/A381304.seq
5b39c3dcab735002fe19c38a89dfe25a
A381305
E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)^(1/2)) / A(x)^(3/2) ).
[ "1", "1", "0", "-1", "-4", "1", "32", "181", "-192", "-4919", "-31616", "88571", "2089984", "13830545", "-83841024", "-1884928471", "-11874992128", "142704083281", "3085703610368", "16806597846295", "-397246640947200", "-8257973126103359", "-32717082633175040", "1686557057210338589", "33490001971564773376" ]
[ "sign" ]
8
0
5
[ "A136630", "A381305" ]
null
Seiichi Manyama, Feb 19 2025
2025-02-20T08:39:42
oeisdata/seq/A381/A381305.seq
0e93051b969f966a1041ddbdc683a6e2
A381306
E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)^(1/2)) / A(x)^(1/2) ).
[ "1", "1", "2", "5", "12", "1", "-416", "-5741", "-60800", "-543719", "-3479424", "6260561", "822338048", "20933340065", "393396789248", "5840683299431", "54344509046784", "-481407806103119", "-44548560374988800", "-1564969488082711811", "-40856692743724335104", "-812774967576805701599", "-8614414458975040831488" ]
[ "sign" ]
9
0
3
[ "A136630", "A381306" ]
null
Seiichi Manyama, Feb 19 2025
2025-02-20T08:39:45
oeisdata/seq/A381/A381306.seq
fdb3a35f32db00e731f6c45d85d36042
A381307
E.g.f. A(x) satisfies A(x) = exp( x * cosh(x * A(x)^(1/2)) ).
[ "1", "1", "1", "4", "25", "126", "841", "8303", "84561", "925480", "12285121", "181409427", "2840445169", "49113986936", "932675641353", "18883732449871", "408771283327969", "9499097097870720", "234457146543484225", "6115077874320445715", "168654204908597822241", "4902220448616467300248" ]
[ "nonn" ]
8
0
4
[ "A185951", "A381307" ]
null
Seiichi Manyama, Feb 19 2025
2025-02-20T08:39:50
oeisdata/seq/A381/A381307.seq
3cb24da6f1e633e56abaaac1aa05b014
A381308
E.g.f. A(x) satisfies A(x) = exp( x * cos(x * A(x)^(1/2)) ).
[ "1", "1", "1", "-2", "-23", "-114", "-119", "4929", "66641", "401320", "-2429759", "-103879555", "-1429782287", "-4427416408", "296377270281", "8315367151441", "97844494408673", "-912681931321984", "-72768121697555135", "-1687481800538833683", "-9411056136574319839", "820910149460546108776" ]
[ "sign" ]
9
0
4
[ "A185951", "A381308" ]
null
Seiichi Manyama, Feb 19 2025
2025-02-20T08:39:54
oeisdata/seq/A381/A381308.seq
3269979e7ced3770224959260fca27e7
A381309
E.g.f. A(x) satisfies A(x) = exp( sinh(x * A(x)^(1/2)) / A(x)^(1/2) ).
[ "1", "1", "1", "2", "9", "42", "209", "1381", "11121", "96744", "936337", "10323865", "125245457", "1640739336", "23339285601", "359236548033", "5918755368865", "103922094286976", "1941594484205793", "38448924176712705", "803753373207738337", "17693469280066921736", "409266060724837855057", "9922356658347766201841" ]
[ "nonn" ]
8
0
4
[ "A136630", "A381309" ]
null
Seiichi Manyama, Feb 19 2025
2025-02-20T08:39:58
oeisdata/seq/A381/A381309.seq
ed9bc7a897edc5fdad5f23770b3325a4
A381310
E.g.f. A(x) satisfies A(x) = exp( sin(x * A(x)^(1/2)) / A(x)^(1/2) ).
[ "1", "1", "1", "0", "-7", "-38", "-111", "259", "7025", "59752", "209297", "-2545257", "-59541487", "-609139048", "-1257456543", "86370090271", "1968628674465", "20998208227456", "-60103780767519", "-7806917233342465", "-175430347192682527", "-1683391495632464904", "26661441929560502097", "1550891419460475900175" ]
[ "sign" ]
8
0
5
[ "A136630", "A381310" ]
null
Seiichi Manyama, Feb 19 2025
2025-02-20T08:40:02
oeisdata/seq/A381/A381310.seq
c6fc2d4e6aa0a4177a88aae4c8ffbf48
A381311
Numbers whose powerful part (A057521) is a power of a prime with an even exponent >= 2.
[ "4", "9", "12", "16", "18", "20", "25", "28", "44", "45", "48", "49", "50", "52", "60", "63", "64", "68", "75", "76", "80", "81", "84", "90", "92", "98", "99", "112", "116", "117", "121", "124", "126", "132", "140", "147", "148", "150", "153", "156", "162", "164", "169", "171", "172", "175", "176", "188", "192", "198", "204", "207", "208", "212", "220", "228", "234", "236" ]
[ "nonn", "easy" ]
12
1
1
[ "A001248", "A030514", "A030516", "A030629", "A030631", "A054753", "A056798", "A057521", "A085987", "A118914", "A178739", "A179644", "A179645", "A179668", "A179672", "A179693", "A179747", "A189982", "A189983", "A189985", "A189987", "A190110", "A190292", "A190388", "A190641", "A246655", "A350388", "A377816", "A381311", "A381312" ]
null
Amiram Eldar, Feb 19 2025
2025-02-21T08:23:47
oeisdata/seq/A381/A381311.seq
414ba6a421900891fcb483b701f8a84b
A381312
Numbers whose powerful part (A057521) is a power of a prime with an odd exponent >= 3 (A056824).
[ "8", "24", "27", "32", "40", "54", "56", "88", "96", "104", "120", "125", "128", "135", "136", "152", "160", "168", "184", "189", "224", "232", "243", "248", "250", "264", "270", "280", "296", "297", "312", "328", "343", "344", "351", "352", "375", "376", "378", "384", "408", "416", "424", "440", "456", "459", "472", "480", "486", "488", "512", "513", "520", "536", "544" ]
[ "nonn", "easy" ]
13
1
1
[ "A030078", "A050997", "A056824", "A057521", "A065036", "A079395", "A092759", "A118914", "A138031", "A178740", "A179664", "A179665", "A179667", "A179670", "A179692", "A179696", "A179704", "A189975", "A189984", "A190378", "A190383", "A190473", "A190641", "A268335", "A301517", "A374459", "A381311", "A381312" ]
null
Amiram Eldar, Feb 19 2025
2025-02-21T08:23:56
oeisdata/seq/A381/A381312.seq
d79383f8e0ac0d9568320e838776aa05
A381313
Numbers that are divisible by the cube of an odd prime.
[ "27", "54", "81", "108", "125", "135", "162", "189", "216", "243", "250", "270", "297", "324", "343", "351", "375", "378", "405", "432", "459", "486", "500", "513", "540", "567", "594", "621", "625", "648", "675", "686", "702", "729", "750", "756", "783", "810", "837", "864", "875", "891", "918", "945", "972", "999", "1000", "1026", "1029", "1053", "1080", "1107", "1125" ]
[ "nonn", "easy" ]
8
1
1
[ "A000265", "A002117", "A038838", "A046099", "A233091", "A381313" ]
null
Amiram Eldar, Feb 19 2025
2025-02-21T08:13:27
oeisdata/seq/A381/A381313.seq
3d7546f34cc58746b269d2582cf66312
A381314
Powerful numbers that have a single exponent in their prime factorization that equals 2.
[ "4", "9", "25", "49", "72", "108", "121", "144", "169", "200", "288", "289", "324", "361", "392", "400", "500", "529", "576", "675", "784", "800", "841", "961", "968", "972", "1125", "1152", "1323", "1352", "1369", "1372", "1568", "1600", "1681", "1849", "1936", "2025", "2209", "2304", "2312", "2500", "2704", "2809", "2888", "2916", "3087", "3136", "3200" ]
[ "nonn", "easy" ]
8
1
1
[ "A001248", "A001694", "A036966", "A065483", "A143610", "A179646", "A179689", "A179699", "A189988", "A189990", "A190106", "A190115", "A190470", "A190471", "A377816", "A377818", "A381314" ]
null
Amiram Eldar, Feb 19 2025
2025-02-21T08:15:26
oeisdata/seq/A381/A381314.seq
61eec94cff6f3c3d1146b4eb7a8cd714
A381315
Numbers whose prime factorization exponents include exactly one 3 and no exponent greater than 3.
[ "8", "24", "27", "40", "54", "56", "72", "88", "104", "108", "120", "125", "135", "136", "152", "168", "184", "189", "200", "232", "248", "250", "264", "270", "280", "296", "297", "312", "328", "343", "344", "351", "360", "375", "376", "378", "392", "408", "424", "440", "456", "459", "472", "488", "500", "504", "513", "520", "536", "540", "552", "568", "584", "594" ]
[ "nonn", "easy" ]
7
1
1
[ "A002117", "A030078", "A046100", "A048109", "A065036", "A143610", "A163569", "A176297", "A179670", "A179695", "A179700", "A189975", "A189984", "A190109", "A190378", "A190382", "A375072", "A375145", "A381315" ]
null
Amiram Eldar, Feb 19 2025
2025-02-21T08:16:49
oeisdata/seq/A381/A381315.seq
a3e1a0a9c76a2bb7546bbb7e2371f578
A381316
Numbers whose powerful part (A057521) is a power of a prime with an exponent >= 3 (A246549).
[ "8", "16", "24", "27", "32", "40", "48", "54", "56", "64", "80", "81", "88", "96", "104", "112", "120", "125", "128", "135", "136", "152", "160", "162", "168", "176", "184", "189", "192", "208", "224", "232", "240", "243", "248", "250", "256", "264", "270", "272", "280", "296", "297", "304", "312", "320", "328", "336", "343", "344", "351", "352", "368", "375", "376", "378" ]
[ "nonn", "easy" ]
10
1
1
[ "A013661", "A030078", "A030514", "A030516", "A030629", "A030631", "A050997", "A056824", "A057521", "A060687", "A065036", "A079395", "A092759", "A138031", "A178739", "A178740", "A179644", "A179645", "A179664", "A179665", "A179667", "A179668", "A179670", "A179672", "A179692", "A179693", "A179696", "A179704", "A179747", "A189975", "A189984", "A189987", "A190110", "A190292", "A190378", "A190383", "A190388", "A190473", "A190641", "A246549", "A344653", "A345193", "A369632", "A381312", "A381316" ]
null
Amiram Eldar, Feb 19 2025
2025-02-21T08:24:05
oeisdata/seq/A381/A381316.seq
4c81370764a5991ebb857fa74b7659ac
A381317
Numbers of the form p^(p +- 1), where p is prime.
[ "2", "8", "9", "81", "625", "15625", "117649", "5764801", "25937424601", "3138428376721", "23298085122481", "3937376385699289", "48661191875666868481", "14063084452067724991009", "104127350297911241532841", "37589973457545958193355601", "907846434775996175406740561329", "480250763996501976790165756943041" ]
[ "nonn", "easy" ]
9
1
1
[ "A036878", "A104126", "A381215", "A381317" ]
null
Paolo Xausa, Feb 20 2025
2025-02-21T06:10:28
oeisdata/seq/A381/A381317.seq
8a593d4b7b8fd9fe2aa2f438f7a8110c
A381319
Order of linear recurrence with constant coefficients of solutions of k satisfying k^(n-1) == 1 (mod n^2) for a given n.
[ "2", "3", "2", "5", "2", "7", "2", "3", "2", "11", "2", "13", "2", "5", "2", "17", "2", "19", "2", "5", "2", "23", "2", "5", "2", "3", "4", "29", "2", "31", "2", "5", "2", "5", "2", "37", "2", "5", "2", "41", "2", "43", "2", "9", "2", "47", "2", "7", "2", "5", "4", "53", "2", "5", "2", "5", "2", "59", "2", "61", "2", "5", "2", "17", "6", "67", "2", "5", "4", "71", "2", "73", "2", "5", "4", "5", "2", "79", "2", "3", "2", "83", "2", "17", "2", "5", "2", "89" ]
[ "nonn" ]
36
2
1
[ "A056020", "A056021", "A056022", "A056024", "A056025", "A056028", "A056031", "A056034", "A056035", "A063994", "A381319" ]
null
Mike Sheppard, Feb 20 2025
2025-04-10T08:37:24
oeisdata/seq/A381/A381319.seq
6da3ab617f27bd0109e225cc498364ce