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 1-8 of 8 results.

A127263 Numbers k such that k^3 divides 2^(k^2)+1.

Original entry on oeis.org

1, 3, 57, 32547, 9961491, 297381939, 1338104811, 3942759027, 5688011361, 8920514307, 9146532873, 40253706489, 243640690617, 764039295291, 1127102902923, 1556475424971, 2251315404417, 3005607686883, 5222670270483
Offset: 1

Views

Author

Max Alekseyev, Mar 27 2007, Mar 29 2007, Apr 18 2007

Keywords

Comments

If k belongs to this sequence, then so does (2^(k^2)+1)/k^2.
From Alexander Adamchuk, May 14 2010: (Start)
3 divides a(n) for n>1.
19 divides a(n) for n>2. (End)

Links

Crossrefs

Cf. A006521, A093546, A093665, A136372, A128677.
Cf. A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685, A177813, A177814, A177816, A177817, A177818, A177819, A177820.

Programs

  • Mathematica
    Select[Range[100000], Divisible[2^(#^2) + 1, #^3] &] (* Robert Price, Mar 23 2020 *)

Extensions

a(7) from Ryan Propper, Jan 01 2008
a(8)-a(19) from Max Alekseyev, May 14 2010

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

Original entry on oeis.org

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

Views

Author

Alexander Adamchuk, May 14 2010

Keywords

Comments

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

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

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

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

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
Showing 1-8 of 8 results.

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