This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A306507 #25 Feb 28 2024 10:46:14
%S A306507 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 A306507 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 A306507 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,113
%N A306507 a(n) = gcd(n!^2+1, sigma(n!)), where sigma() denotes the sum of the divisors.
%C A306507 A sequence that produces primes.
%C A306507 A counterexample is found at n=7880, here the gcd is 380927609 = 15761*24169.
%C A306507 Interesting properties may be found in this sequence, for example many primes are 2n+1.
%F A306507 a(n) = gcd(A020549(n), A062569(n)).
%t A306507 Table[GCD[(n!)^2+1,DivisorSigma[1,n!]],{n,90}] (* _Harvey P. Dale_, Jun 03 2021 *)
%o A306507 (PARI) a(n) = gcd(n!^2+1, sigma(n!)); \\ _Michel Marcus_, Feb 20 2019
%Y A306507 Cf. A000203, A020549, A062569.
%K A306507 nonn
%O A306507 1,6
%A A306507 _Daoudi Rédoane_, Feb 20 2019
%E A306507 More terms from _Michel Marcus_, Feb 20 2019