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.
%I A127643 #8 Aug 16 2021 22:05:11
%S A127643 15,51,65,85,185,221,255,341,451,533,561,595,645,679,771,1059,1095,
%T A127643 1105,1271,1285,1313,1387,1455,1581,1729,1905,2045,2047,2091,2307,
%U A127643 2465,2701,2755,2821,2895,3201,3205,3277,3281,3341,3603,3655,3723,3855,4033,4039
%N A127643 Composite numbers k that divide A123591(k) = ((2^k - 1)^(2^k) - 1)/(2^k)^2.
%C A127643 p divides A123591(p) for prime p > 2.
%C A127643 Odd composite numbers k such that (2^k-1)^(2^k) == 1 (mod k). - _Robert Israel_, Jul 06 2017
%H A127643 Robert Israel, <a href="/A127643/b127643.txt">Table of n, a(n) for n = 1..571</a>
%p A127643 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 A127643 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 A127643 Cf. A123591, A085606.
%K A127643 nonn
%O A127643 1,1
%A A127643 _Alexander Adamchuk_, Jan 22 2007