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 1-3 of 3 results.

A014960 Integers n such that n divides 24^n - 1.

Original entry on oeis.org

1, 23, 529, 1081, 12167, 24863, 50807, 279841, 571849, 1168561, 2387929, 2870377, 6436343, 7009273, 13152527, 15954479, 26876903, 54922367, 66018671, 112232663, 134907719, 148035889, 161213279, 302508121, 329435831
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

Also, numbers n such that n divides s(n), where s(1)=1, s(k)=s(k-1)+k*24^(k-1) (cf. A014942).
All n > 1 in the sequence are multiple of 23. - Conjectured by Thomas Baruchel, Oct 10 2003; proved by Max Alekseyev, Nov 16 2019
If n is a term and prime p|(24^n - 1), then n*p is a term. In particular, if n is a term and prime p|n, then n*p is a term. The smallest term with 3 distinct prime factors is a(16) = 15954479 = 23 * 47 * 14759. - Max Alekseyev, Nov 16 2019

Links

Crossrefs

Prime factors are listed in A087807.
Cf. A014942.
Integers n such that n divides b^n - 1: A067945 (b=3), A014945 (b=4), A067946 (b=5), A014946 (b=6), A067947 (b=7), A014949 (b=8), A068382 (b=9), A014950 (b=10), A068383 (b=11), A014951 (b=12), A116621 (b=13), A014956 (b=14), A177805 (b=15), A014957 (b=16), A177807 (b=17), A128358 (b=18), A125000 (b=19), A128360 (b=20), A014959 (b=22).

Programs

  • Mathematica
    s = 1; Do[ If[ Mod[ s, n ] == 0, Print[n]]; s = s + (n + 1)*24^n, {n, 1, 100000}]
Join[{1},Select[Range[330*10^6],PowerMod[24,#,#]==1&]] (* Harvey P. Dale, Jan 19 2023 *)

Extensions

More terms from Robert G. Wilson v, Sep 13 2000
a(9)-a(12) from Thomas Baruchel, Oct 10 2003
Edited and terms a(13) onward added by Max Alekseyev, Nov 16 2019

A014962 Odd numbers k that divide 25^k - 1.

Original entry on oeis.org

1, 3, 9, 21, 27, 63, 81, 93, 147, 171, 189, 243, 279, 441, 513, 567, 609, 651, 729, 837, 903, 1029, 1197, 1323, 1539, 1701, 1827, 1953, 2187, 2511, 2667, 2709, 2883, 2943, 3087, 3249, 3591, 3969, 4263, 4401, 4557, 4617, 5103, 5301, 5481, 5859, 6321
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

Also, numbers k such that k divides s(k), where s(1)=1, s(j) = s(j-1) + j*25^(j-1).
Equivalently, numbers k that divide ((24*k - 1)*25^k + 1) / 24^2 (cf. A014943).

Links

Crossrefs

Cf. A014943, A014945, A014946, A014949, A014950, A014951, A014956, A014957, A128358, A128360, A014959, A014960.

Programs

  • Maple
    select(t -> 25 &^ t - 1 mod t = 0, [seq(i,i=1..10^4,2)]); # Robert Israel, Oct 04 2020

Extensions

Edited by Max Alekseyev, Nov 16 2019

A133027 Divisors of 1701.

Original entry on oeis.org

1, 3, 7, 9, 21, 27, 63, 81, 189, 243, 567, 1701
Offset: 1

Views

Author

Omar E. Pol, Oct 27 2007

Keywords

Examples

			27*63 = 1701.

Links

Crossrefs

Cf. A003594, A014854, A014959, A018326, A018522, A056745, A057233, A057263, A057286, A057493, A118564, A125227.

Programs

Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.