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 10 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

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

A292338 Numbers k such that k^2 divides 13^k + 1.

Original entry on oeis.org

1, 7, 203, 11977, 154553, 353423, 4482037, 9904979, 20851957, 69262991, 264440183, 6824905927, 7803226417, 17244568439, 47773414171, 57280493557, 120586867331, 197922271883, 218692031341, 249815987281, 409580786629, 460390358603, 802768833013, 963574941161, 1003238606531, 1146808373599, 1385429010959, 1529257578289
Offset: 1

Views

Author

Max Alekseyev, Sep 16 2017

Keywords

Links

Crossrefs

Subsequence of A015963.
Cf. A128393, A177813.

A292392 Numbers n such that n^2 divides (17^n + 1).

Original entry on oeis.org

1, 3, 9, 21, 39, 63, 117, 273, 819, 2067, 3081, 6201, 9243, 12807, 14469, 21567, 43407, 48711, 50877, 64701, 89649, 146133, 149331, 163293, 166491, 221169, 340977, 356139, 447993, 489879, 546819, 661401, 663507, 1022931, 1143051, 1165437, 1548183, 1639911, 1640457
Offset: 1

Views

Author

K. D. Bajpai, Sep 15 2017

Keywords

Comments

After a(1), all the terms are multiples of 3.
From Robert Israel, Sep 18 2017: (Start)
All terms are odd.
If m and n are terms then lcm(m,n) is a term.
If n is a term not divisible by 9, then 3n is a term. (End)

Examples

			3 appears is a term because 3^2 divides (17^3 + 1): 4914/9 = 546.
9 appears is a term because 9^2 divides (17^9 + 1): 118587876498/81 = 1464047858.

Crossrefs

Cf. A015951, A123047, A123052, A177813, A292331.

Programs

  • Maple
    A292392:= proc(n) if(17 &^ n+1)mod (n^2)=0  then RETURN (n); fi; end: seq(A292392(n), n=1..50000);
  • Mathematica
    Select[Range[50000], IntegerQ[(PowerMod[17, #, #^2] + 1)/#^2] &]
  • PARI
    for(n=1, 5e6, if (Mod(17, n^2)^n==-1, print1(n, ", ")));
  • PARI
    is(n) = Mod(17, n^2)^n==-1 \\ Felix Fröhlich, Sep 16 2017
Showing 1-10 of 10 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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