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 A326577 #19 Apr 26 2024 03:18:14
%S A326577 1,3,5,7,3,11,13,3,17,19,3,23,5,3,29,31,3,1,37,3,41,43,15,47,7,3,53,1,
%T A326577 3,59,61,3,5,67,3,71,73,3,1,79,3,83,5,3,89,7,3,1,97,3,101,103,15,107,
%U A326577 109,3,113,1,3,1,11,3,5,127,3,131,7,3,137,139,3,1,5
%N A326577 a(n) = (2*n - 1) / A326478(2*n - 1).
%H A326577 Amiram Eldar, <a href="/A326577/b326577.txt">Table of n, a(n) for n = 1..10000</a>
%F A326577 If 2*n - 1 is prime then a(n) is prime.
%F A326577 a(n) = gcd((2*n-1)*N(2*n-2), D(2*n-2)), with N(k)/D(k) = B(k) the k-th Bernoulli number.
%p A326577 A326577 := n -> (2*n - 1)/A326478(2*n - 1): seq(A326577(n), n=1..72);
%p A326577 db := n -> denom(bernoulli(n)): nb := n -> numer(bernoulli(n)):
%p A326577 a := n -> igcd(db(2*n-2), (2*n-1)*nb(2*n-2)): seq(a(n), n=1..72);
%t A326577 a[n_] := Module[{b = BernoulliB[2*n -2]}, (2* n - 1) * Denominator[b] / ((2 * n - 1) * Denominator[(2 * n - 1) * b])]; Array[a, 100] (* _Amiram Eldar_, Apr 26 2024 *)
%o A326577 (PARI) f(n) = n*denominator(n*bernfrac(n-1))/denominator(bernfrac(n-1)); \\ A326478
%o A326577 a(n) = (2*n-1)/f(2*n-1); \\ _Michel Marcus_, Jul 17 2019
%Y A326577 Cf. A326478, A326578, A027641/A027642 (Bernoulli).
%K A326577 nonn
%O A326577 1,2
%A A326577 _Peter Luschny_, Jul 16 2019