A127263 -id:A127263 - cp's OEIS frontend

A177813 Numbers k such that k^3 divides 13^(k^2) + 1.

1, 7, 203, 11977, 154553, 353423, 3049963, 4482037, 5192537, 7170569, 9904979, 20851957, 33461911, 35852033, 69262991, 88448927, 160274303, 264440183, 306359683, 381231473, 423063571, 978466699, 1974252749, 2115269947, 4647954787, 5218486693, 6824905927, 7803226417, 9040206917, 10041409007, 11055712717, 12483960629, 17244568439, 47773414171, 57280493557, 57729535241, 58257187051, 62418389453, 67340133077

Offset: 1

Alexander Adamchuk, May 14 2010

nonn

7 divides a(n) for n > 1.

Prime factors of a(n) in the order of their appearance are {7, 29, 59, 22079, 1741, 435709, 25579, 35323, 827, 164837, 176611, 5783, 435709, 22896329, 54461639, 4820033, ...}. - Alexander Adamchuk, May 16 2010

Cf. A127263 (k^3 divides 2^(k^2) + 1).
Cf. A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685.
Cf. A177813, A177814, A177816, A177817, A177818, A177819, A177820.
Cf. A128677 (least k > p such that (k*p)^3 divides (p-1)^(k*p)^2+1, where p = prime(n) > 2).

Corrected and extended by Max Alekseyev, May 16 2010
a(8) = 4482037 (suggested by Max Alekseyev) missing in original sequence inserted by Alexander Adamchuk, May 16 2010
More terms from Max Alekseyev, Feb 14 2012

A177814 Numbers k such that k^3 divides 14^(k^2) + 1.

Original entry on oeis.org

1, 3, 5, 15, 57, 183, 285, 355, 505, 915, 1065, 1515, 2005, 2265, 3477, 6015, 10887, 12165, 17385, 20005, 20235, 27015, 28785, 35855, 43035, 54435, 60015, 64965, 92415, 107565, 114285, 134139, 138165, 142355, 160815, 201995, 202505, 228765

Offset: 1

Alexander Adamchuk, May 14 2010

nonn

Cf. A127263 (k^3 divides 2^(k^2) + 1).
Cf. A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685.
Cf. A177813, A177814, A177816, A177817, A177818, A177819, A177820.
Cf. A128677 (least k > p such that (k*p)^3 divides (p-1)^(k*p)^2+1, where p = prime(n) > 2).

A177816 Numbers k such that k^3 divides 16^(k^2) + 1.

Original entry on oeis.org

1, 17, 707489, 5030929, 6029713, 209372172193, 250938565921, 1413292053713, 1784415176081, 24025953593297, 48948914347889, 1423524187400657, 5817190224008753, 49446116858851553, 74262006382962977

Offset: 1

Alexander Adamchuk, May 14 2010

nonn

17 divides a(n) for n > 1.

Cf. A127263 (k^3 divides 2^(k^2) + 1).
Cf. A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685.
Cf. A177813, A177814, A177816, A177817, A177818, A177819, A177820.
Cf. A128677 (least k > p such that (k*p)^3 divides (p-1)^(k*p)^2+1, where p = prime(n) > 2).

Terms a(6) onward from Max Alekseyev, May 16 2010

A177817 Numbers k such that k^3 divides 17^(k^2) + 1.

Original entry on oeis.org

1, 3, 9, 21, 39, 63, 117, 273, 819, 1467, 2067, 3081, 4269, 6201, 7299, 9243, 10269, 12807, 14469, 16959, 19071, 20421, 21567, 23877, 29883, 43407, 48711, 50877, 51093, 55497, 64701, 89649, 94887, 118713, 133497, 142947, 146133, 149331

Offset: 1

Alexander Adamchuk, May 14 2010

nonn

3 divides a(n) for n > 1.

Cf. A127263 (k^3 divides 2^(k^2) + 1).
Cf. A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685.
Cf. A177813, A177814, A177816, A177817, A177818, A177819, A177820.
Cf. A128677 (least k > p such that (k*p)^3 divides (p-1)^(k*p)^2+1, where p = prime(n) > 2).

A177818 Numbers k such that k^3 divides 18^(k^2) + 1.

Original entry on oeis.org

1, 19, 397841, 1152331, 3566699, 24128658809, 74683110361, 216316727651, 1339092172657, 7967201553697

Offset: 1

Alexander Adamchuk, May 14 2010

19 divides a(n) for n > 1.

Cf. A127263 (k^3 divides 2^(k^2) + 1).
Cf. A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685.
Cf. A177813, A177814, A177816, A177817, A177818, A177819, A177820.
Cf. A128677 (least k > p such that (k*p)^3 divides (p-1)^(k*p)^2+1, where p = prime(n) > 2).

a(6)-a(10) from Max Alekseyev, May 16 2010

A177819 Numbers k such that k^3 divides 19^(k^2) + 1.

Original entry on oeis.org

1, 5, 55, 1265, 11255, 59455, 123805, 395755, 635255, 874115, 1028555, 1456015, 2847515, 3201715, 3841805, 4353305, 6655055, 6987805, 13443155, 16825765, 23656765, 36370015, 41083405, 66919765, 68432705, 100126015, 123012395

Offset: 1

Alexander Adamchuk, May 14 2010

nonn

5 divides a(n) for n > 1.

Cf. A127263 (k^3 divides 2^(k^2) + 1).
Cf. A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685.
Cf. A177813, A177814, A177816, A177817, A177818, A177819, A177820.
Cf. A128677 (least k > p such that (k*p)^3 divides (p-1)^(k*p)^2+1, where p = prime(n) > 2).

Select[Range[123020000],PowerMod[19,#^2,#^3]==#^3-1&] (* Harvey P. Dale, May 20 2021 *)

More terms from Max Alekseyev, May 16 2010

A177820 Numbers k such that k^3 divides 20^(k^2) + 1.

Original entry on oeis.org

1, 3, 7, 21, 381, 903, 921, 2667, 5789, 6447, 17367, 18543, 73703, 114681, 116967, 208443, 221109, 277221, 746781, 797349, 818769, 855141, 871347, 1459101, 2205609, 2354961, 5090367, 5331669, 5692701, 6099429, 7611387, 8710041

Offset: 1

Alexander Adamchuk, May 14 2010

nonn

Cf. A127263 (k^3 divides 2^(k^2) + 1).
Cf. A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685.
Cf. A177813, A177814, A177816, A177817, A177818, A177819, A177820.
Cf. A128677 (least k > p such that (k*p)^3 divides (p-1)^(k*p)^2+1, where p = prime(n) > 2).

A136373 Primes dividing terms of A128685.

Original entry on oeis.org

13, 79, 4057, 36037, 222379, 973597, 1310611, 2070433, 4381183, 4905427, 8145943651, 21843304081, 66988402183

Offset: 1

Alexander Adamchuk, Dec 27 2007

Cf. A128685, A127263, A136372, A128677, A128678, A128679, A128680, A128681, A128682, A128683, A128684.

Edited and extended by Max Alekseyev, May 14 2010

A136374 a(n) = (A128677(n) - 1)/(2*A000040(n)).

Original entry on oeis.org

3, 4, 2, 1, 3, 1224, 551, 1, 697, 66, 60, 31, 12, 7, 24641820, 3343240, 122610, 134, 4, 101, 80, 1, 979, 518, 1414

Offset: 2

Alexander Adamchuk, Dec 27 2007

All terms are integer since for n > 1, p = A000040(n) divides (A128677(n)-1)/2.

			a(2) = (A128677(2) - 1)/(2*A000040(2)) = (19 - 1)/(2*3) = 3.

Cf. A128677, A127263, A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685.

a(n) = (A128677(n) - 1)/(2*A000040(n)).

a(16)-a(26) from Max Alekseyev, May 14 2010

cp's OEIS Frontend

A177813 Numbers k such that k^3 divides 13^(k^2) + 1.

Views

Author

Keywords

Comments

Crossrefs

Extensions

A177814 Numbers k such that k^3 divides 14^(k^2) + 1.

Views

Author

Keywords

Crossrefs

A177816 Numbers k such that k^3 divides 16^(k^2) + 1.

Views

Author

Keywords

Comments

Crossrefs

Extensions

A177817 Numbers k such that k^3 divides 17^(k^2) + 1.

Views

Author

Keywords

Comments

Crossrefs

A177818 Numbers k such that k^3 divides 18^(k^2) + 1.

Views

Author

Keywords

Comments

Crossrefs

Extensions

A177819 Numbers k such that k^3 divides 19^(k^2) + 1.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Extensions

A177820 Numbers k such that k^3 divides 20^(k^2) + 1.

Views

Author

Keywords

Crossrefs

A136373 Primes dividing terms of A128685.

Views

Author

Keywords

Crossrefs

Extensions

A136374 a(n) = (A128677(n) - 1)/(2*A000040(n)).

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula

Extensions