A068468 Decimal expansion of zeta(6)/(zeta(2)*zeta(3)).

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

Offset: 0

Author

Benoit Cloitre, Mar 10 2002

Keywords

• cons
• easy
• nonn

Examples

			0.514510101508393123073281186772789616506565746907128.....
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Index entries for zeta function.

Crossrefs

Cf. A013661 (zeta(2)), A002117 (zeta(3)), A013664 (zeta(6)), A082695 (inverse).

Programs

Magma

R:=RealField(150); SetDefaultRealField(R); L:=RiemannZeta(); 2*Pi(R)^4/(315*Evaluate(L,3)); // G. C. Greubel, Mar 11 2018

Mathematica

RealDigits[Zeta[6]/(Zeta[2]*Zeta[3]), 10, 100][[1]] (* G. C. Greubel, Mar 11 2018 *)

PARI

default(realprecision, 100); zeta(6)/(zeta(2)*zeta(3)) \\ G. C. Greubel, Mar 11 2018

Formula

From Amiram Eldar, Nov 07 2022: (Start)

Equals 2*Pi^4/(315*zeta(3)).

Equals Product_{p prime} (1 - 1/(p^2-p+1)). (End)