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A343367
Decimal expansion of 1/zeta(7).
2
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
0,1
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
LINKS
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
EXAMPLE
0.9917198558384443104281859314975506916499...
MATHEMATICA
RealDigits[1/Zeta[7], 10, 100][[1]] (* Amiram Eldar, Apr 13 2021 *)
PROG
(PARI) 1/zeta(7) \\ A.H.M. Smeets, Apr 13 2021
CROSSREFS
Sequence in context: A175618 A346439 A266555 * A145280 A144667 A118428
KEYWORD
nonn,cons
AUTHOR
Karl-Heinz Hofmann, Apr 12 2021
STATUS
approved