A093595 a(n) = numerator of Sum_{k in A030059} 1/k^(2n).
9, 15, 11340, 278775, 16247385, 37139825022300, 7581939039675, 76731473729479944375, 3915591422490399696806136375, 381397512477801513050979496875, 16227546388799797830522276658125, 67515115618959321499592977317448539337500, 20377345777534646475773937030353201765625
Offset: 1
Examples
9/(2*Pi^2), 15/(2*Pi^4), 11340/(691*Pi^6), 278775/(7234*Pi^8), ...
References
- 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)).
Links
- Eric Weisstein's World of Mathematics, Prime Sums.
Programs
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Mathematica
Numerator[Table[(Zeta[2*n]^2 - Zeta[4*n]) / (2*Zeta[2*n]*Zeta[4*n]), {n, 1, 12}]] (* Amiram Eldar, Jan 19 2025 *)
Formula
a(n) = numerator((zeta(2n)^2-zeta(4n))/(2*zeta(2n)*zeta(4n))).
Comments