A343367 Decimal expansion of 1/zeta(7).

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

Offset: 0

Author

Karl-Heinz Hofmann, Apr 12 2021

Keywords

• nonn
• cons

Comments

Decimal expansion of 1/zeta(7), the inverse of A013665.

1/zeta(7) has no known closed-form formula like 1/zeta(2) = 6/Pi^2, 1/zeta(4) = 90/Pi^4 or 1/zeta(6) = 945/Pi^6.

1/zeta(7) is the probability that 7 randomly selected numbers will be coprime. - A.H.M. Smeets, Apr 13 2021

Examples

			0.9917198558384443104281859314975506916499...
		

Links

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

Crossrefs

Cf. A008683, A013665.

Programs

Mathematica

RealDigits[1/Zeta[7], 10, 100][[1]] (* Amiram Eldar, Apr 13 2021 *)

PARI

1/zeta(7) \\ A.H.M. Smeets, Apr 13 2021

Formula

Equals 1/A013665.

Equals Sum_{k>=1} mobius(k) / k^7. - Sean A. Irvine, Aug 20 2021

Equals Product_{p prime} (1 - 1/p^7). - Amiram Eldar, Jun 01 2023