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 A330279 #34 Aug 02 2023 07:21:09 %S A330279 27,51,65,69,75,111,123,129,147,153,171,175,185,189,195,207,231,237, %T A330279 243,245,267,275,279,285,291,303,309,315,321,343,363,365,369,387,395, %U A330279 405,411,417,425,429,435,441,447,489,495,505,507,519,531,555,567,573,591,597 %N A330279 Numbers k such that x^k == k (mod k + 1) has multiple solutions for 0 <= x < k. %C A330279 All odd numbers have k^k == k (mod k + 1), but only some have other solutions in the least residue system (e.g. 3^27 and 19^27 == 27 (mod 28)). %C A330279 Odd numbers k such that k and A000010(k+1) are not coprime. - _Robert Israel_, Jul 30 2023 %H A330279 Robert Israel, <a href="/A330279/b330279.txt">Table of n, a(n) for n = 1..10000</a> %H A330279 Robert Israel et al, <a href="https://math.stackexchange.com/questions/4743587/even-k-such-that-xk-equiv-1-mod-k1-has-solutions">Even k such that x^k == -1 mod k has solutions</a> %e A330279 27 is in the list because x^27 == 27 (mod 28) has three solutions: 3, 19, and 27. %p A330279 select(t -> igcd(t,numtheory:-phi(t+1))>1, [seq(i,i=1..1000,2)]); # _Robert Israel_, Jul 30 2023 %t A330279 ok[k_] := Length[Select[Range[0, k-1], PowerMod[#, k, k + 1] == k &, 2]] > 1; Select[ Range@ 600, ok] (* _Giovanni Resta_, Dec 10 2019 *) %o A330279 (PARI) isok(k) = sum(i=0, k-1, Mod(i, k+1)^k == k) > 1; \\ _Michel Marcus_, Dec 10 2019 %Y A330279 Cf. A000010, A014117, A096008, A195637. %K A330279 nonn %O A330279 1,1 %A A330279 _Christopher Cormier_, Dec 09 2019