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A343359
Decimal expansion of 1/zeta(6).
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
0,1
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
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)
EXAMPLE
0.982952592264580419804896564993924132951221515986...
MATHEMATICA
RealDigits[1/Zeta[6], 10, 100][[1]] (* Amiram Eldar, Apr 12 2021 *)
PROG
(PARI) 1/zeta(6) \\ A.H.M. Smeets, Apr 13 2021
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Karl-Heinz Hofmann, Apr 12 2021
STATUS
approved