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A342683
Decimal expansion of 1/zeta(8).
2
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
0,1
COMMENTS
1/zeta(8) is the probability that 8 randomly selected numbers will be coprime.
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)
EXAMPLE
0.9959392011255151468348364728055453240050227784589...
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 *)
PROG
(PARI) 1/zeta(8)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Karl-Heinz Hofmann, May 18 2021
STATUS
approved