A157289 Decimal expansion of Zeta(3)/Zeta(6).

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

Offset: 1

Author

R. J. Mathar, Feb 26 2009

Keywords

• cons
• nonn

Comments

The Product_{p = primes = A000040} (1+1/p^3), the cubic analog to A082020.

Examples

			1.181564949010256912569399734... = (1+1/2^3)*(1+1/3^3)*(1+1/5^3)*(1+1/7^3)*...
		

Crossrefs

Cf. A002117, A005117, A013664, A030078, A062838, A082020.

Programs

Maple

evalf(Zeta(3)/Zeta(6)) ;

Mathematica

RealDigits[Zeta[3]/Zeta[6],10,120][[1]] (* Harvey P. Dale, Jul 23 2016 *)

Formula

Equals A002117/A013664 = Product_{i} (1+1/A030078(i)).

Equals Sum_{k>=1} 1/A062838(k) = Sum_{k>=1} 1/A005117(k)^3. - Amiram Eldar, May 22 2020