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%I #31 Dec 26 2020 03:56:18
%S 561,2821,838201,41471521,45496270561,776388344641,344361421401361,
%T 375097930710820681,330019822807208371201
%N The smallest Carmichael number k such that phi(k) does not divide (k-1)^n, where phi is the Euler totient function.
%C Conjecture: phi(a(n)) divides (a(n)-1)^(n+1).
%C a(10) <= 9645020063586019926451. - _Daniel Suteu_, Dec 25 2020
%H José María Grau and Antonio M. Oller-Marcén, <a href="http://arxiv.org/abs/1012.2337">On k-Lehmer numbers</a>, Integers, 12(2012), #A37.
%H Nathan McNew, <a href="http://arxiv.org/abs/1210.2001">Radically weakening the Lehmer and Carmichael conditions</a> (2012).
%o (PARI) is_c(n) = { my(f); bittest(n, 0) && !for(i=1, #f=factor(n)~, (f[2, i]==1 && n%(f[1, i]-1)==1)||return) && #f>1; }
%o isok(k, n) = ((k-1)^n % eulerphi(k)) != 0;
%o a(n) = my(k=1); while (!(is_c(k) && isok(k,n)), k++); k; \\ _Michel Marcus_, Dec 25 2020
%Y Cf. A000010, A002997 (Carmichael numbers), A173703.
%K nonn,more
%O 1,1
%A _José María Grau Ribas_, Feb 15 2012
%E a(7)-a(9) from _Richard Pinch_, Feb 18 2012
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