A343359 Decimal expansion of 1/zeta(6).

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

Offset: 0

Author

Karl-Heinz Hofmann, Apr 12 2021

Keywords

• nonn
• cons

Comments

Decimal expansion of 1/zeta(6), the inverse of A013664.

1/zeta(6) has a known closed-form formula (945/Pi^6) like 1/zeta(2) = 6/Pi^2 and 1/zeta(4) = 90/Pi^4.

1/zeta(6) is the probability that 6 randomly selected numbers will be coprime. - A.H.M. Smeets, Apr 13 2021

Examples

			0.982952592264580419804896564993924132951221515986...
		

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, A088453, A215267, A343308.

Programs

Mathematica

RealDigits[1/Zeta[6], 10, 100][[1]] (* Amiram Eldar, Apr 12 2021 *)

PARI

1/zeta(6) \\ A.H.M. Smeets, Apr 13 2021

Formula

Equals 1/A013664 = 945/Pi^6.

From Amiram Eldar, Jun 01 2023: (Start)

Equals Sum_{k>=1} mu(k)/k^6, where mu is the Möbius function (A008683).

Equals Product_{p prime} (1 - 1/p^6). (End)