A341901 Decimal expansion of 1/zeta(9).

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

Offset: 0

Author

Karl-Heinz Hofmann, Jun 04 2021

Keywords

• nonn
• cons

Comments

1/zeta(9) is the probability that 9 randomly selected numbers will be coprime.

Examples

			0.997995632730762156864676132105099996320941848...
		

Links

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

Crossrefs

Cf. A008683, A013667, A059956, A088453, A215267, A343308, A343359, A343367, A342683.

Programs

Mathematica

RealDigits[1/Zeta[9], 10, 100][[1]]

PARI

1/zeta(9)

Formula

Equals 1/A013667.

From Amiram Eldar, Jun 01 2023: (Start)

Equals Sum_{k>=1} mu(k)/k^9, where mu is the Möbius function (A008683).

Equals Product_{p prime} (1 - 1/p^9). (End)