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%I #22 Jan 19 2023 19:45:55
%S 1,23,529,1081,12167,24863,50807,279841,571849,1168561,2387929,
%T 2870377,6436343,7009273,13152527,15954479,26876903,54922367,66018671,
%U 112232663,134907719,148035889,161213279,302508121,329435831
%N Integers n such that n divides 24^n - 1.
%C Also, numbers n such that n divides s(n), where s(1)=1, s(k)=s(k-1)+k*24^(k-1) (cf. A014942).
%C All n > 1 in the sequence are multiple of 23. - Conjectured by _Thomas Baruchel_, Oct 10 2003; proved by _Max Alekseyev_, Nov 16 2019
%C 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
%H Max Alekseyev, <a href="/A014960/b014960.txt">Table of n, a(n) for n = 1..146</a>
%t s = 1; Do[ If[ Mod[ s, n ] == 0, Print[n]]; s = s + (n + 1)*24^n, {n, 1, 100000}]
%t Join[{1},Select[Range[330*10^6],PowerMod[24,#,#]==1&]] (* _Harvey P. Dale_, Jan 19 2023 *)
%Y Prime factors are listed in A087807.
%Y Cf. A014942.
%Y 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).
%K nonn
%O 1,2
%A _Olivier Gérard_
%E More terms from _Robert G. Wilson v_, Sep 13 2000
%E a(9)-a(12) from _Thomas Baruchel_, Oct 10 2003
%E Edited and terms a(13) onward added by _Max Alekseyev_, Nov 16 2019
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