cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

A106305 Divisors of 10^14 - 1.

Original entry on oeis.org

1, 3, 9, 11, 33, 99, 239, 717, 2151, 2629, 4649, 7887, 13947, 23661, 41841, 51139, 153417, 460251, 909091, 1111111, 2727273, 3333333, 8181819, 9999999, 10000001, 12222221, 30000003, 36666663, 90000009, 109999989, 217272749, 651818247
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Oct 12 2005

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A001270, A007138, A046107, A112505.

Programs

Formula

10^14 - 1 = 3^2 * 11 * 239 * 4649 * 909091 = 99999999999999. - Alonso del Arte, Nov 09 2017

A109933 Divisors of 10^13 - 1.

Original entry on oeis.org

1, 3, 9, 53, 79, 159, 237, 477, 711, 4187, 12561, 37683, 265371653, 796114959, 2388344877, 14064697609, 20964360587, 42194092827, 62893081761, 126582278481, 188679245283, 1111111111111, 3333333333333, 9999999999999
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Oct 11 2005

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A001270, A007138, A046107.

Programs

A111117 Divisors of 10^15 - 1.

Original entry on oeis.org

1, 3, 9, 27, 31, 37, 41, 93, 111, 123, 271, 279, 333, 369, 813, 837, 999, 1107, 1147, 1271, 1517, 2439, 3441, 3813, 4551, 7317, 8401, 10027, 10323, 11111, 11439, 13653, 25203, 30081, 30969, 33333, 34317, 40959, 47027, 75609, 90243, 99999, 141081
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Oct 15 2005

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A001270, A007138, A046107, A112505.

Programs

A111211 Divisors of 10^16 - 1.

Original entry on oeis.org

1, 3, 9, 11, 17, 33, 51, 73, 99, 101, 137, 153, 187, 219, 303, 411, 561, 657, 803, 909, 1111, 1233, 1241, 1507, 1683, 1717, 2329, 2409, 3333, 3723, 4521, 5151, 6987, 7227, 7373, 9999, 10001, 11169, 13563, 13651, 13837, 15453, 18887, 20961, 22119, 25619
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Oct 25 2005

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A111117, A001270, A007138, A046107, A112505.

Programs

A113522 Divisors of 10^18 - 1.

Original entry on oeis.org

1, 3, 7, 9, 11, 13, 19, 21, 27, 33, 37, 39, 57, 63, 77, 81, 91, 99, 111, 117, 133, 143, 171, 189, 209, 231, 247, 259, 273, 297, 333, 351, 399, 407, 429, 481, 513, 567, 627, 693, 703, 741, 777, 819, 891, 999, 1001, 1053, 1197, 1221, 1287, 1443, 1463, 1539, 1729
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Jan 12 2006

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A111117, A111211, A113116, A001270, A007138, A046107, A112505.

Programs

A245027 Divisors of 7^12 - 1.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 19, 20, 24, 25, 26, 30, 32, 36, 38, 39, 40, 43, 45, 48, 50, 52, 57, 60, 65, 72, 75, 76, 78, 80, 86, 90, 95, 96, 100, 104, 114, 117, 120, 129, 130, 144, 150, 152, 156, 160, 171, 172, 180, 181, 190, 195, 200, 208
Offset: 1

Views

Author

Bruno Berselli, Jul 10 2014

Keywords

Comments

Number of divisors of k^12-1 for k = 2..20: 24 (2), 80 (3), 96 (4), 240 (5), 128 (6), 864 (7), 512 (8), 384 (9), 256 (10), 1920 (11), 256 (12), 960 (13), 384 (14), 448 (15), 768 (16), 1792 (17), 768 (18), 3840 (19), 384 (20).
The following triangular numbers belong to this sequence: 1, 3, 6, 10, 15, 36, 45, 78, 120, 171, 190, 300, 325, 741, 780, 2080, 2850, 4560, 8385, 14706, 16290, 5915080, 1730160900.

Examples

			13841287200 = 2^5 * 3^2 * 5^2 * 13 * 19 * 43 * 181.

Links

Crossrefs

Cf. Divisors of k^12-1: A003524 (k=2); A003532 (k=4); A003543 (k=8), A027902 (k=9), A027897 (k=10), A245028 (k=11).

Programs

  • Magma
    Divisors(7^12-1);
  • Mathematica
    Divisors[7^12 - 1]
  • Maxima
    divisors(7^12-1);
  • PARI
    divisors(7^12-1)
  • Sage
    divisors(7^12-1)

A113116 Divisors of 10^17 - 1.

Original entry on oeis.org

1, 3, 9, 2071723, 6215169, 18645507, 5363222357, 16089667071, 48269001213, 11111111111111111, 33333333333333333, 99999999999999999
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Jan 02 2006

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A111117, A111211, A001270, A007138, A046107, A112505.

Programs

A226477 Table (read by rows) of the natural numbers (in ascending order) whose reciprocals have only periodic decimals of length k.

Original entry on oeis.org

1, 3, 9, 11, 33, 99, 27, 37, 111, 333, 999, 101, 303, 909, 1111, 3333, 9999, 41, 123, 271, 369, 813, 2439, 11111, 33333, 99999, 7, 13, 21, 39, 63, 77, 91, 117, 143, 189, 231, 259, 273, 297, 351, 407, 429, 481, 693, 777, 819, 1001, 1221, 1287, 1443, 2079, 2331, 2457, 2849, 3003, 3367, 3663, 3861, 4329, 5291, 6993, 8547, 9009, 10101, 10989, 12987, 15873, 25641, 27027, 30303, 37037, 47619, 76923, 90909, 111111, 142857, 333333, 999999
Offset: 1

Views

Author

Martin Renner, Jun 08 2013

Keywords

Comments

The k-th row always ends with 10^k - 1 = 99..99 (k times 9).
The number of elements in row k is A059892(k).

Examples

			The table T(k,m), m = 1..A059892(k), begins
  1, 3, 9;
  11, 33, 99;
  27, 37, 111, 333, 999;
  etc.

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A111117, A111211, A113116, A113522 (Divisors of 10^k - 1, k = 2..18), A059892, A084680.

Programs

  • Maple
    a:=[1,3,9]: S:={1,3,9}: for k from 2 to 6 do T:=numtheory[divisors](10^k-1): a:=[op(a),op(T minus S)]: S:=S union T; od: a;
  • PARI
    Row(n) = my(v=divisors(10^n-1)); select(x->(znorder(Mod(10,x))==n), v) \\ Jianing Song, Jun 15 2021

A245028 Divisors of 11^12 - 1.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 24, 26, 28, 30, 35, 36, 37, 38, 39, 40, 42, 45, 48, 52, 56, 57, 60, 61, 63, 65, 70, 72, 74, 76, 78, 80, 84, 90, 91, 95, 104, 105, 111, 112, 114, 117, 120, 122, 126, 130, 133, 140, 144, 148, 152
Offset: 1

Views

Author

Bruno Berselli, Jul 10 2014

Keywords

Comments

See Comments section in A245027.
The following 36 triangular numbers belong to this sequence: 1, 3, 6, 10, 15, 21, 28, 36, 45, 78, 91, 105, 120, 171, 190, 210, 630, 666, 703, 741, 780, 1596, 1830, 4095, 4560, 5460, 6216, 16653, 33670, 46360, 103740, 115440, 221445, 274170, 365085, 392303547090.
The following terms of A001082 (without 1, 21 and 120, which appear in the previous list) are in sequence: 5, 8, 16, 40, 56, 65, 133, 208, 280, 456, 481, 560, 936, 1008, 1281, 1365, 1680, 1776, 1976, 4880, 5985, 10920, 11285, 44408, 47880, 590520, 658008, 731120, 973560, 1046142792240.
Also, 4/5 of the members are divisible by 3 and 2/3 of them are even.

Examples

			3138428376720 = 2^4 * 3^2 * 5 * 7 * 13 * 19 * 37 * 61 * 1117.

Links

Crossrefs

Cf. Divisors of k^12-1: A003524 (k=2); A003532 (k=4); A245027 (k=7), A003543 (k=8), A027902 (k=9), A027897 (k=10).

Programs

  • Magma
    Divisors(11^12-1);
  • Mathematica
    Divisors[11^12 - 1]
  • Maxima
    divisors(11^12-1);
  • PARI
    divisors(11^12-1)
  • Sage
    divisors(11^12-1)
Showing 1-9 of 9 results.

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