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

1,1

Comments

See the Hardy reference, p. 65, fourth formula (with a misprint corrected), and the Weisstein link, eqs. (25)-(31). - Wolfdieter Lang, Oct 18 2016

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

Table of n, a(n) for n=1..13.

Eric Weisstein's World of Mathematics, Prime Sums.

Formula

a(n) = numerator((zeta(2n)^2-zeta(4n))/(2*zeta(2n)*zeta(4n))).

Example

9/(2*Pi^2), 15/(2*Pi^4), 11340/(691*Pi^6), 278775/(7234*Pi^8), ...

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 *)

Crossrefs

Cf. A030059, A093596 (denominators).

Sequence in context: A100241 A078794 A373332 * A330429 A372213 A215418

Adjacent sequences: A093592 A093593 A093594 * A093596 A093597 A093598

Keyword

nonn,easy,frac

Author

Eric W. Weisstein, Apr 03 2004

Status

approved