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