A127092 -id:A127092 - cp's OEIS frontend

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

1, 17, 128583032925805678351

Offset: 1

Alexander Adamchuk, Mar 08 2007

17 divides a(n) for n > 1.

a(4) > 10^50. - Max Alekseyev, Mar 01 2025

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.

A128399 Numbers k such that k^2 divides 19^k-1.

Original entry on oeis.org

1, 2, 3, 4, 6, 9, 10, 12, 18, 20, 30, 36, 42, 60, 84, 90, 110, 126, 156, 180, 210, 220, 252, 294, 330, 381, 420, 468, 588, 630, 660, 724, 762, 780, 882, 930, 990, 1092, 1143, 1260, 1332, 1470, 1510, 1524, 1764, 1806, 1830, 1860, 1980, 2028, 2058, 2172, 2286, 2310

Offset: 1

Alexander Adamchuk, Mar 01 2007

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..5000

Columns k=19 of A333500.

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

Join[{1},Select[Range[3000],PowerMod[19,#,#^2]==1&]] (* Harvey P. Dale, Oct 24 2017 *)

for(k=1, 1e4, if(Mod(19, k^2)^k==1, print1(k", "))) \\ Seiichi Manyama, Mar 25 2020

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

Alexander Adamchuk, Mar 08 2007

19 divides a(n) for n > 1.

Subsequence of A128360.

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

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

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

Alexander Adamchuk, Mar 01 2007

13 divides all except the first term.

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

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

Alexander Adamchuk, Mar 01 2007

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

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 *)

A177917 Numbers k such that k^3 divides 17^(k^2) - 1.

Original entry on oeis.org

1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 40, 42, 48, 58, 60, 72, 78, 80, 84, 90, 110, 114, 116, 120, 126, 144, 156, 168, 174, 180, 210, 220, 222, 228, 232, 234, 240, 252, 290, 312, 330, 336, 342, 348, 360, 390, 420, 440, 444, 456, 464, 468, 504, 522, 546

Offset: 1

Alexander Adamchuk, May 14 2010

nonn

The first 9 terms (and others) of A218087 are in this sequence A177917 as well as in A128397. These two sequences have many terms in common, but A177917 \ A128397 = {10, 30, 58, 90, 110, ...} and A128397 \ A177917 = {580, 624, 660, 684, 696, 720, ...}. - M. F. Hasler, Oct 22 2012

Robert Price, Table of n, a(n) for n = 1..6436

Cf. A129211, A129212, A177905, A177907, A127102, A177909, A177243, A177911, A177912, A177913, A177914, A177915, A177916, A177918, A177919, A177920.

Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, ..., A128397.

Select[Range[600],Divisible[17^#^2-1,#^3]&] (* Harvey P. Dale, Jul 19 2015 *)

is_A177917(n)=Mod(17,n^3)^(n^2)==1  \\ M. F. Hasler, Oct 21 2012

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

Alexander Adamchuk, Mar 01 2007

Daniel Starodubtsev, Table of n, a(n) for n = 1..1000

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

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

Alexander Adamchuk, Mar 01 2007

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

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

Alexander Adamchuk, Mar 01 2007

11 divides all except the first term.

All terms are congruent to +-1 (mod 12). - Robert G. Wilson v, Dec 19 2014

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

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 *)

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

Alexander Adamchuk, Mar 01 2007

Amiram Eldar, Table of n, a(n) for n = 1..640

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

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 *)

is(k) = Mod(15, k^2)^k == 1; \\ Amiram Eldar, May 21 2024

More terms from Stefan Steinerberger, Jun 10 2007

cp's OEIS Frontend

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

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A128399 Numbers k such that k^2 divides 19^k-1.

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

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

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

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A177917 Numbers k such that k^3 divides 17^(k^2) - 1.

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

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

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

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

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