A157291 - OEIS

%I #16 May 22 2020 16:21:45

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

%T 6,8,4,2,4,7,8,8,4,2,5,6,0,7,6,8,9,4,8,0,8,2,2,4,6,6,5,4,2,3,7,4,4,6,

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

%N Decimal expansion of Zeta(5)/Zeta(10).

%C The product_{p = primes = A000040} (1+1/p^5), the fifth-power analog to A082020.

%F Equals A013663/A013668 = Product_{i>=1} (1+1/A050997(i)).

%F Equals Sum_{k>=1} 1/A005117(k)^5 = 1 + Sum_{k>=1} 1/A113850(k). - _Amiram Eldar_, May 22 2020

%F Equals 93555 * zeta(5) / Pi^10. - _Vaclav Kotesovec_, May 22 2020

%e 1.035897477277500224... = (1+1/2^5)*(1+1/3^5)*(1+1/5^5)*(1+1/7^5)*...

%p evalf(Zeta(5)/Zeta(10)) ;

%t RealDigits[Zeta[5]/Zeta[10],10,120][[1]] (* _Harvey P. Dale_, Apr 06 2013 *)

%Y Cf. A013663, A013668, A050997, A082020.

%Y Cf. A005117, A113850.

%K cons,easy,nonn

%O 1,3

%A _R. J. Mathar_, Feb 26 2009