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
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
KEYWORD
cons,nonn
AUTHOR
Benoit Cloitre, May 24 2005
STATUS
approved