A107370 Decimal expansion of 8*Pi^4/(21*zeta(3)).

3, 0, 8, 7, 0, 6, 0, 6, 0, 9, 0, 5, 0, 3, 5, 8, 7, 3, 8, 4, 3, 9, 6, 8, 7, 1, 2, 0, 6, 3, 6, 7, 3, 7, 6, 9, 9, 0, 3, 9, 3, 9, 4, 4, 8, 1, 4, 4, 2, 7, 6, 8, 1, 1, 0, 0, 2, 5, 2, 6, 0, 7, 4, 3, 3, 3, 4, 7, 3, 0, 8, 9, 6, 9, 6, 2, 9, 4, 9, 6, 8, 0, 6, 3, 9, 4, 3, 0, 5, 4, 8, 7, 2, 1, 2, 5, 5, 8, 4, 8, 8, 5, 0, 7, 9

Offset

2,1

Comments

sum(k<N,r_3(k)^2) is asymptotic to 8*Pi^4*N^2/(21*zeta(3)) where r_3(n) is the number of representations of a positive integer n as a sum of 3 squares of integers.

Links

Table of n, a(n) for n=2..106.

S. K. K. Choi, A. V. Kumchev and R. Osburn, On sums of three squares, arXiv:math/0502007 [math.NT], 2005.

Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 18.

Formula

30.870606090503587...

Mathematica

RealDigits[(8*Pi^4)/(21*Zeta[3]), 10, 120][[1]] (* Harvey P. Dale, Nov 29 2014 *)

Prog

(PARI) 8*Pi^4/21/zeta(3)

Crossrefs

Cf. A005875.

Sequence in context: A137204 A021328 A178114 * A201580 A234518 A068458

Adjacent sequences: A107367 A107368 A107369 * A107371 A107372 A107373

Keyword

cons,nonn

Author

Benoit Cloitre, May 24 2005

Status

approved