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Sequence gives values of gcd(k!+1, k^k-1) when not equal to 1 in order of appearance.
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%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