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%I #8 Aug 16 2021 22:05:11
%S 15,51,65,85,185,221,255,341,451,533,561,595,645,679,771,1059,1095,
%T 1105,1271,1285,1313,1387,1455,1581,1729,1905,2045,2047,2091,2307,
%U 2465,2701,2755,2821,2895,3201,3205,3277,3281,3341,3603,3655,3723,3855,4033,4039
%N Composite numbers k that divide A123591(k) = ((2^k - 1)^(2^k) - 1)/(2^k)^2.
%C p divides A123591(p) for prime p > 2.
%C Odd composite numbers k such that (2^k-1)^(2^k) == 1 (mod k). - _Robert Israel_, Jul 06 2017
%H Robert Israel, <a href="/A127643/b127643.txt">Table of n, a(n) for n = 1..571</a>
%p select(n -> not isprime(n) and (2^n-1) &^ (2^n) mod n = 1, [seq(i,i=9..10000,2)]); # _Robert Israel_, Jul 06 2017
%t Do[f=PowerMod[(2^n-1),(2^n),n]-1;If[ !PrimeQ[n]&&IntegerQ[(n+1)/2]&&IntegerQ[f/n],Print[n]],{n,2,10000}]
%Y Cf. A123591, A085606.
%K nonn
%O 1,1
%A _Alexander Adamchuk_, Jan 22 2007
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