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 1-10 of 17 results. Next

A128393 Numbers k such that k^2 divides 13^k - 1.

Original entry on oeis.org

1, 2, 3, 4, 6, 12, 14, 20, 28, 42, 60, 68, 84, 140, 183, 204, 220, 340, 366, 406, 420, 476, 660, 732, 812, 942, 1020, 1218, 1428, 1540, 1806, 1860, 1884, 2380, 2436, 2562, 3612, 3660, 3740, 4060, 4620, 5060, 5124, 6594, 7004, 7140, 8420, 9420, 9940, 11220
Offset: 1

Views

Author

Alexander Adamchuk, Mar 01 2007

Keywords

Links

Crossrefs

Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128405, A128394, A128395, A128396, A128397, A128398, A128399, A128400, A128401, A128402, A128403, A128404.

Programs

  • Mathematica
    Join[{1},Select[Range[12000],PowerMod[13,#,#^2]==1&]] (* Harvey P. Dale, Sep 05 2012 *)

A128397 Numbers k such that k^2 divides 17^k-1.

Original entry on oeis.org

1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 36, 40, 42, 48, 60, 72, 78, 80, 84, 116, 120, 126, 144, 156, 168, 180, 220, 232, 234, 240, 252, 312, 336, 342, 348, 360, 420, 440, 464, 468, 504, 546, 580, 624, 660, 684, 696, 720, 780, 840, 880, 936, 1008, 1044, 1092, 1160
Offset: 1

Views

Author

Alexander Adamchuk, Mar 01 2007

Keywords

Comments

The first 9 numbers (and many more) which are a multiple of their digital sum in all bases from 2 through 16 (A218087), are members of this sequence, and also of A177917. - M. F. Hasler, Oct 22 2012

Links

Crossrefs

Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128405, A128393, A128394, A128395, A128396, A128398, A128399, A128400, A128401, A128402, A128403, A128404.
Cf. A177917.

Programs

A128398 Numbers k such that k^2 divides 18^k - 1.

Original entry on oeis.org

1, 17, 128583032925805678351
Offset: 1

Views

Author

Alexander Adamchuk, Mar 08 2007

Keywords

Comments

17 divides a(n) for n > 1.
a(4) > 10^50. - Max Alekseyev, Mar 01 2025

Crossrefs

Subsequence of A128358.
Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128405, A128393, A128394, A128395, A128396, A128397, A128398, A128399, A128400, A128401, A128402, A128403, A128404.

A128400 Numbers k such that k^2 divides 20^k - 1.

Original entry on oeis.org

1, 19, 1432001198261, 3661225986659, 275941052631578947368421, 43838606653900416716028459121, 26357241068661238901986943659181
Offset: 1

Views

Author

Alexander Adamchuk, Mar 08 2007

Keywords

Comments

19 divides a(n) for n > 1.
Subsequence of A128360.

Crossrefs

Cf. A128360, A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128405, A128393, A128394, A128395, A128396, A128397, A128398, A128399, A128400, A128401, A128402, A128403, A128404.

Programs

  • PARI
    for( n=1, 10^6, Mod(20,n^2)^n - 1 || print1(n",")) \\ M. F. Hasler, Oct 20 2008

Extensions

a(4) from Max Alekseyev, Oct 18 2008
a(5)-a(7) from Max Alekseyev, May 06 2010

A128394 Numbers k such that k^2 divides 14^k - 1.

Original entry on oeis.org

1, 13, 2041, 24355253, 249302027, 16772956369, 39665616523, 388885239223, 2974921088191, 3487599163841, 61054982558011, 200151688351277, 473329801968959
Offset: 1

Views

Author

Alexander Adamchuk, Mar 01 2007

Keywords

Comments

13 divides all except the first term.

Crossrefs

Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128405, A128393, A128395, A128396, A128397, A128398, A128399, A128400, A128401, A128402, A128403, A128404.

Extensions

a(4)-a(5) from Farideh Firoozbakht, Mar 05 2007
a(6)-a(13) from Max Alekseyev, May 06 2010

A128396 Numbers k such that k^2 divides 16^k-1.

Original entry on oeis.org

1, 3, 5, 15, 21, 39, 55, 105, 155, 165, 195, 205, 273, 465, 609, 615, 903, 915, 1155, 1265, 1365, 1705, 2067, 2145, 2255, 2265, 2373, 2667, 3045, 3081, 3255, 3795, 4305, 4515, 4895, 4965, 5115, 6045, 6123, 6355, 6405, 6765, 7077, 7455, 7917, 7995, 10065
Offset: 1

Views

Author

Alexander Adamchuk, Mar 01 2007

Keywords

Links

Crossrefs

Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128405, A128393, A128394, A128396, A128397, A128398, A128399, A128400, A128401, A128402, A128403, A128404.

Programs

  • Mathematica
    Select[Range[11000],Divisible[16^#-1,#^2]&] (* Harvey P. Dale, Dec 14 2010 *)
Join[{1},Select[Range[11000],PowerMod[16,#,#^2]==1&]] (* Harvey P. Dale, Mar 16 2022 *)

A128401 Numbers k such that k^2 divides 21^k-1.

Original entry on oeis.org

1, 2, 4, 5, 10, 20, 22, 44, 52, 68, 110, 220, 260, 340, 506, 572, 748, 820, 884, 1012, 2530, 2756, 2860, 3740, 3916, 4108, 4420, 5060, 9020, 9724, 10660, 13156, 13780, 13940, 17204, 19580, 20540, 23782, 29084, 30316, 34060, 45188, 46852, 47564
Offset: 1

Views

Author

Alexander Adamchuk, Mar 01 2007

Keywords

Links

Crossrefs

Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128405, A128393, A128394, A128395, A128396, A128397, A128398, A128399, A128400, A128402, A128403, A128404.

Programs

  • Mathematica
    Select[Range[50000],Divisible[21^#-1,#^2]&] (* Harvey P. Dale, Jun 17 2011 *)

A128403 Numbers k such that k^2 divides 23^k-1.

Original entry on oeis.org

1, 2, 4, 6, 8, 11, 12, 20, 22, 24, 40, 42, 44, 60, 66, 78, 84, 88, 120, 132, 156, 168, 212, 220, 264, 312, 420, 424, 440, 444, 462, 474, 546, 620, 636, 660, 780, 820, 840, 858, 888, 924, 948, 1014, 1060, 1092, 1218, 1220, 1240, 1272, 1320, 1560, 1640, 1716
Offset: 1

Views

Author

Alexander Adamchuk, Mar 01 2007

Keywords

Links

Crossrefs

Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128405, A128393, A128394, A128395, A128396, A128397, A128398, A128399, A128400, A128401, A128402, A128404.

Programs

  • Mathematica
    Join[{1},Select[Range[2000],PowerMod[23,#,#^2]==1&]] (* Harvey P. Dale, May 02 2015 *)

A128405 Numbers k such that k^2 divides 12^k - 1.

Original entry on oeis.org

1, 11, 253, 11891, 768361, 36112967, 61488361, 154261943, 2936791979, 61057324141, 67546215517, 107342336783, 186740152357, 347036920549, 429306186947, 468493520891, 635974117823, 797688507253, 3174672129299
Offset: 1

Views

Author

Alexander Adamchuk, Mar 01 2007

Keywords

Comments

11 divides all except the first term.
All terms are congruent to +-1 (mod 12). - Robert G. Wilson v, Dec 19 2014

Crossrefs

Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128393, A128394, A128395, A128396, A128397, A128398, A128399, A128400, A128401, A128402, A128403, A128404.

Programs

  • Mathematica
    fQ[n_] := Mod[ PowerMod[12, n, n^2] - 1, n^2] == 0; k = 1; lst = {}; While[k < 100000001, If[ fQ@ k, AppendTo[lst, k]; Print@ k]; k += 10; If[ fQ@ k, AppendTo[lst, k]; Print@ k]; k += 2]; lst (* Robert G. Wilson v, Dec 19 2014 *)

Extensions

a(6)-a(8) from Farideh Firoozbakht, Mar 05 2007
Terms a(9) onward from Max Alekseyev, May 06 2010

A128395 Numbers k such that k^2 divides 15^k-1.

Original entry on oeis.org

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 136, 272, 452, 812, 904, 952, 1624, 1808, 1904, 3164, 3248, 6328, 11912, 12656, 15368, 18632, 23824, 27608, 30736, 37264, 47908, 55216, 60248, 83384, 91756, 95816, 102604, 107576, 113936, 120496, 130424, 166768
Offset: 1

Views

Author

Alexander Adamchuk, Mar 01 2007

Keywords

Links

Crossrefs

Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128405, A128393, A128395, A128396, A128397, A128398, A128399, A128400, A128401, A128402, A128403, A128404.

Programs

  • Mathematica
    a={1};For[n=1,n<200000,n++,If[PowerMod[15,n,n^2]==1, AppendTo[a, n]]]; a (* Stefan Steinerberger, Jun 10 2007 *)
Join[{1},Select[Range[167000],PowerMod[15,#,#^2]==1&]] (* Harvey P. Dale, Sep 14 2020 *)
  • PARI
    is(k) = Mod(15, k^2)^k == 1; \\ Amiram Eldar, May 21 2024

Extensions

More terms from Stefan Steinerberger, Jun 10 2007
Showing 1-10 of 17 results. Next

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