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A343367 Decimal expansion of 1/zeta(7).

%I A343367 #42 Jun 01 2023 01:58:34
%S A343367 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,
%T A343367 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,
%U A343367 9,8,3,9,2,2,7,3,9,5,8,0,0,3,0,7,8,8,7,4
%N A343367 Decimal expansion of 1/zeta(7).
%C A343367 Decimal expansion of 1/zeta(7), the inverse of A013665.
%C A343367 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.
%C A343367 1/zeta(7) is the probability that 7 randomly selected numbers will be coprime. -  _A.H.M. Smeets_, Apr 13 2021
%H A343367 Karl-Heinz Hofmann, <a href="/A343367/b343367.txt">Table of n, a(n) for n = 0..10000</a>
%H A343367 Wikipedia, <a href="https://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann zeta function</a>.
%F A343367 Equals 1/A013665.
%F A343367 Equals Sum_{k>=1} mobius(k) / k^7. - _Sean A. Irvine_, Aug 20 2021
%F A343367 Equals Product_{p prime} (1 - 1/p^7). - _Amiram Eldar_, Jun 01 2023
%e A343367 0.9917198558384443104281859314975506916499...
%t A343367 RealDigits[1/Zeta[7], 10, 100][[1]] (* _Amiram Eldar_, Apr 13 2021 *)
%o A343367 (PARI) 1/zeta(7) \\ _A.H.M. Smeets_, Apr 13 2021
%Y A343367 Cf. A008683, A013665.
%K A343367 nonn,cons
%O A343367 0,1
%A A343367 _Karl-Heinz Hofmann_, Apr 12 2021