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%I #22 Feb 20 2024 09:23:30
%S 1,5427,41255,43755,208161,496175,497135
%N Numbers k such that gcd(k! + 1, k^k + 1) is neither 1 nor 2k+1.
%C g(n) = gcd(n! + 1, n^n + 1) is almost always equal to 1 or to 2n+1. These are the known exceptions: g(1) = 2, g(5427) = 10453, g(41255) = 129341, g(43755) = 157519, g(208161) = 555097. - _Hans Havermann_, Mar 28 2006
%C a(8) > 1000000. - _Nick Hobson_, Feb 20 2024
%e gcd(1! + 1, 1^1 + 1) = 2 and 2 != 2*1 + 1, so 1 belongs to the sequence.
%o (C) See Links section in A116893.
%Y Cf. A014566, A038507, A067658, A116891, A116892, A116893.
%K nonn,hard,more
%O 1,2
%A _Giovanni Resta_, Mar 01 2006
%E a(5) from _Hans Havermann_, Mar 28 2006
%E a(6)-a(7) from _Nick Hobson_, Feb 20 2024
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