cp's OEIS Frontend

A269404 Decimal expansion of Product_{k >= 1} (1 + 1/prime(k)^6).

%I A269404 #20 Feb 16 2025 08:33:30
%S A269404 1,0,1,7,0,9,2,7,6,9,1,3,0,4,9,9,2,7,6,6,4,3,2,7,2,1,3,3,0,9,7,9,0,9,
%T A269404 9,2,0,4,9,2,2,1,9,0,7,9,4,9,4,1,0,1,1,3,4,6,6,4,6,5,1,7,9,3,8,1,8,9,
%U A269404 3,5,3,3,5,8,3,4,2,2,7,9,4,3,1,8,1,5,1,5,9,6,4,7,8,5,0,6,6,8,9,7,8,4,5,4,6,5,1,0,6,4,0,2,6,1,3,3,6,9,3,0
%N A269404 Decimal expansion of Product_{k >= 1} (1 + 1/prime(k)^6).
%C A269404 More generally, Product_{k >= 1} (1 + 1/prime(k)^m) = zeta(m)/zeta(2*m), where zeta(m) is the Riemann zeta function.
%H A269404 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeProducts.html">Prime Products</a>.
%F A269404 Equals zeta(6)/zeta(12).
%F A269404 Equals 675675/(691*Pi^6).
%F A269404 Equals Sum_{k>=1} 1/A005117(k)^6 = 1 + Sum_{k>=1} 1/A113851(k). - _Amiram Eldar_, Jun 27 2020
%e A269404 1.0170927691304992766432721330979099204922190794941...
%t A269404 RealDigits[Zeta[6]/Zeta[12], 10, 120][[1]]
%t A269404 RealDigits[675675/(691 Pi^6), 10, 120][[1]]
%o A269404 (PARI) zeta(6)/zeta(12) \\ _Amiram Eldar_, Jun 11 2023
%Y A269404 Cf. A005117, A082020, A113851, A157289, A157290, A157291.
%K A269404 nonn,cons
%O A269404 1,4
%A A269404 _Ilya Gutkovskiy_, Feb 25 2016