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%I #25 Feb 28 2024 10:46:14
%S 1,1,1,1,1,13,1,17,1,1,1,1,1,1,1,1,1,1,1,1,61,1,1,1,1,1,1,1,1,61,1,1,
%T 1,193,1,1,1,757,61,1,1,1,1,1,1,1,1,1,1,1,1,1,1,109,1,1,1,181,1,1,1,1,
%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,113
%N a(n) = gcd(n!^2+1, sigma(n!)), where sigma() denotes the sum of the divisors.
%C A sequence that produces primes.
%C A counterexample is found at n=7880, here the gcd is 380927609 = 15761*24169.
%C Interesting properties may be found in this sequence, for example many primes are 2n+1.
%F a(n) = gcd(A020549(n), A062569(n)).
%t Table[GCD[(n!)^2+1,DivisorSigma[1,n!]],{n,90}] (* _Harvey P. Dale_, Jun 03 2021 *)
%o (PARI) a(n) = gcd(n!^2+1, sigma(n!)); \\ _Michel Marcus_, Feb 20 2019
%Y Cf. A000203, A020549, A062569.
%K nonn
%O 1,6
%A _Daoudi Rédoane_, Feb 20 2019
%E More terms from _Michel Marcus_, Feb 20 2019
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