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.

Previous Showing 11-20 of 20 results.

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

Views

Author

Alexander Adamchuk, May 14 2010

Keywords

Crossrefs

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

Views

Author

Alexander Adamchuk, May 14 2010

Keywords

Comments

17 divides a(n) for n > 1.

Crossrefs

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).

Extensions

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

Views

Author

Alexander Adamchuk, May 14 2010

Keywords

Comments

3 divides a(n) for n > 1.

Crossrefs

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

Views

Author

Alexander Adamchuk, May 14 2010

Keywords

Comments

19 divides a(n) for n > 1.

Crossrefs

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).

Extensions

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

Views

Author

Alexander Adamchuk, May 14 2010

Keywords

Comments

5 divides a(n) for n > 1.

Crossrefs

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).

Programs

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

Extensions

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

Views

Author

Alexander Adamchuk, May 14 2010

Keywords

Crossrefs

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).

A136372 Prime factors of terms of A127263.

Original entry on oeis.org

3, 19, 571, 9137, 41113, 174763, 274081, 1236787, 7485811, 23474953, 34630009, 47822393, 69171211, 92346689, 160465489
Offset: 1

Views

Author

Alexander Adamchuk, Dec 27 2007

Keywords

Comments

From Alexander Adamchuk, May 14 2010: (Start)
3 divides A127263(n) for n > 1.
19 divides A127263(n) for n > 2. (End)

Examples

			A127263(1) = 1,
A127263(2) = 3,
A127263(3) = 57 = 3*19,
A127263(4) = 32547 = 3*19*571,
A127263(5) = 9961491 = 3*19*174763,
A127263(6) = 297381939 = 3*19*571*9137.

Crossrefs

Cf. A127263, A128677, A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685, A136373.
Cf. A177813, A177814, A177816, A177817, A177818, A177819, A177820. - Alexander Adamchuk, May 14 2010

Extensions

Edited and extended by Max Alekseyev, May 14 2010

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

Views

Author

Alexander Adamchuk, Dec 27 2007

Keywords

Crossrefs

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

Extensions

Edited and extended by Max Alekseyev, May 14 2010

A292331 Numbers k such that k^2 divides 5^k + 1.

Original entry on oeis.org

1, 3, 21, 609, 903, 2667, 9429, 26187, 77343, 114681, 159663, 212541, 273441, 405447, 1197483, 1357503, 1398747, 3325749, 4451181, 4630227, 6099429, 6865509, 8620941, 9139263, 11757963, 13047447, 20277201, 26992707, 34727007, 37088709, 38596929, 39367587, 40563663, 51491769, 58372629, 59280123, 63002541, 71688687, 95430909
Offset: 1

Views

Author

Max Alekseyev, Sep 14 2017

Keywords

Links

Crossrefs

Subsequence of A015951.
Cf. A127105, A128679.

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

Views

Author

Alexander Adamchuk, Dec 27 2007

Keywords

Comments

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

Examples

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

Crossrefs

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

Formula

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

Extensions

a(16)-a(26) from Max Alekseyev, May 14 2010
Previous Showing 11-20 of 20 results.

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