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%I #19 Jun 11 2023 02:54:39
%S 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 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 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 Decimal expansion of Product_{k >= 1} (1 + 1/prime(k)^6).
%C More generally, Product_{k >= 1} (1 + 1/prime(k)^m) = zeta(m)/zeta(2*m), where zeta(m) is the Riemann zeta function.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeProducts.html">Prime Products</a>.
%F Equals zeta(6)/zeta(12).
%F Equals 675675/(691*Pi^6).
%F Equals Sum_{k>=1} 1/A005117(k)^6 = 1 + Sum_{k>=1} 1/A113851(k). - _Amiram Eldar_, Jun 27 2020
%e 1.0170927691304992766432721330979099204922190794941...
%t RealDigits[Zeta[6]/Zeta[12], 10, 120][[1]]
%t RealDigits[675675/(691 Pi^6), 10, 120][[1]]
%o (PARI) zeta(6)/zeta(12) \\ _Amiram Eldar_, Jun 11 2023
%Y Cf. A005117, A082020, A113851, A157289, A157290, A157291.
%K nonn,cons
%O 1,4
%A _Ilya Gutkovskiy_, Feb 25 2016