A342683 Decimal expansion of 1/zeta(8).

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

Offset: 0

Author

Karl-Heinz Hofmann, May 18 2021

Keywords

• nonn
• cons

Comments

1/zeta(8) is the probability that 8 randomly selected numbers will be coprime.

Examples

			0.9959392011255151468348364728055453240050227784589...
		

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 0..10000
• Wikipedia, Riemann zeta function.
• Index entries for transcendental numbers

Crossrefs

Cf. A008683, A059956, A215267, A343359, A013666.

Programs

Maple

evalf(9450/Pi^8,100) ; # R. J. Mathar, Jun 04 2021

Mathematica

RealDigits[1/Zeta[8], 10, 100][[1]] (* Amiram Eldar, May 18 2021 *)

PARI

1/zeta(8)

Formula

Equals 1/A013666 = 9450/Pi^8.

From Amiram Eldar, Jun 01 2023: (Start)

Equals Sum_{k>=1} mu(k)/k^8, where mu is the Möbius function (A008683).

Equals Product_{p prime} (1 - 1/p^8). (End)