%I #16 Oct 27 2019 05:20:37
%S 2,3,5,11,7,19,11,13,17,19,43,23,401,29,31,67,37,41,43,47,53,59,61,
%T 131,67,71,73,79,163,83,89,179,97,101,103,107,109,113,227,127,131,137,
%U 139,149,151,157,163,167,173,347,179,181,191,193,197,199,419,211,443,223
%N Sequence gives values of gcd(k!+1, k^k-1) when not equal to 1 in order of appearance.
%C Sequence appears to contain each prime number once or twice.
%F For some even k: gcd(k!+1, k^k-1) = k+1;
%F for some odd k: gcd(k!+1, k^k-1) = 2*k+1.
%e For k=25, gcd(k!+1, k^k-1) = 401;
%e for k=788, gcd(k!+1, k^k-1) = 4729.
%p select(x-> x>1, [seq(igcd(k!+1, k^k-1), k=1..300)])[]; # _Alois P. Heinz_, Oct 26 2019
%K nonn
%O 1,1
%A _Benoit Cloitre_, Feb 03 2002