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 A093595 #17 Feb 16 2025 08:32:53
%S A093595 9,15,11340,278775,16247385,37139825022300,7581939039675,
%T A093595 76731473729479944375,3915591422490399696806136375,
%U A093595 381397512477801513050979496875,16227546388799797830522276658125,67515115618959321499592977317448539337500,20377345777534646475773937030353201765625
%N A093595 a(n) = numerator of Sum_{k in A030059} 1/k^(2n).
%C A093595 See the Hardy reference, p. 65, fourth formula (with a misprint corrected), and the Weisstein link, eqs. (25)-(31). - _Wolfdieter Lang_, Oct 18 2016
%D A093595 G. H. Hardy, Ramanujan, AMS Chelsea Publishing, 2002, pp. 64-65, (misprint on p.65, line starting with Hence: it should be ... -1/Zeta(s) not ... -Zeta(s)).
%H A093595 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeSums.html">Prime Sums</a>.
%F A093595 a(n) = numerator((zeta(2n)^2-zeta(4n))/(2*zeta(2n)*zeta(4n))).
%e A093595 9/(2*Pi^2), 15/(2*Pi^4), 11340/(691*Pi^6), 278775/(7234*Pi^8), ...
%t A093595 Numerator[Table[(Zeta[2*n]^2 - Zeta[4*n]) / (2*Zeta[2*n]*Zeta[4*n]), {n, 1, 12}]] (* _Amiram Eldar_, Jan 19 2025 *)
%Y A093595 Cf. A030059, A093596 (denominators).
%K A093595 nonn,easy,frac
%O A093595 1,1
%A A093595 _Eric W. Weisstein_, Apr 03 2004