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

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

1,2

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

Max Alekseyev, Table of n, a(n) for n = 1..146

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 *)

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).

Sequence in context: A097778 A332797 A057193 * A207230 A207223 A207010

Adjacent sequences: A014957 A014958 A014959 * A014961 A014962 A014963

Keyword

nonn

Author

Olivier Gérard

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

Status

approved