cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A343359 Decimal expansion of 1/zeta(6).

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%I A343359 #40 Jun 01 2023 01:56:23
%S A343359 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,
%T A343359 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,
%U A343359 2,5,4,1,3,4,4,6,8,7,4,2,4,8,0,8,9,8,9,5,5,4
%N A343359 Decimal expansion of 1/zeta(6).
%C A343359 Decimal expansion of 1/zeta(6), the inverse of A013664.
%C A343359 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.
%C A343359 1/zeta(6) is the probability that 6 randomly selected numbers will be coprime. - _A.H.M. Smeets_, Apr 13 2021
%H A343359 Karl-Heinz Hofmann, <a href="/A343359/b343359.txt">Table of n, a(n) for n = 0..10000</a>
%H A343359 Wikipedia, <a href="https://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann zeta function</a>.
%H A343359 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A343359 Equals 1/A013664 = 945/Pi^6.
%F A343359 From _Amiram Eldar_, Jun 01 2023: (Start)
%F A343359 Equals Sum_{k>=1} mu(k)/k^6, where mu is the Möbius function (A008683).
%F A343359 Equals Product_{p prime} (1 - 1/p^6). (End)
%e A343359 0.982952592264580419804896564993924132951221515986...
%t A343359 RealDigits[1/Zeta[6], 10, 100][[1]] (* _Amiram Eldar_, Apr 12 2021 *)
%o A343359 (PARI) 1/zeta(6) \\ _A.H.M. Smeets_, Apr 13 2021
%Y A343359 Cf. A008683, A059956, A088453, A215267, A343308.
%K A343359 nonn,cons
%O A343359 0,1
%A A343359 _Karl-Heinz Hofmann_, Apr 12 2021