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 A093596 #17 Feb 16 2025 08:32:53
%S A093596 2,2,691,7234,174611,163327586881,13571120588,55769228412163778,
%T A093596 1154372017217796891921391,45587914559383477650447161,
%U A093596 786244320265033260236106076,1325861528365506758393998232189714777,162188234491877244039346965481488044,4806877204106337185378935774268985038351236
%N A093596 a(n) = Pi^(2n)*denominator of Sum_{k in A030059} 1/k^(2n).
%H A093596 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeSums.html">Prime Sums</a>.
%F A093596 a(n) = denominator((zeta(2n)^2-zeta(4n))/(2*zeta(2n)*zeta(4n)))/Pi^(2n). See Eqns (28) to (31) of the link.
%e A093596 9/(2*Pi^2), 15/(2*Pi^4), 11340/(691*Pi^6), 278775/(7234*Pi^8), ...
%t A093596 Table[Denominator[(Zeta[2*n]^2 - Zeta[4*n]) / (2*Zeta[2*n]*Zeta[4*n])] / Pi^(2*n), {n, 1, 12}] (* _Amiram Eldar_, Jan 19 2025 *)
%Y A093596 Cf. A030059, A093595 (numerators).
%K A093596 nonn,easy,frac
%O A093596 1,1
%A A093596 _Eric W. Weisstein_, Apr 03 2004