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.
%I A385809 #20 Aug 31 2025 16:31:58
%S A385809 7,0,4,0,7,2,4,8,7,3,2,0,7,8,4,4,7,8,2,9,6,2,9,8,1,9,9,9,7,8,6,2,4,4,
%T A385809 5,8,0,9,2,5,8,3,7,8,1,1,1,9,9,8,8,2,9,3,2,4,2,8,8,4,6,9,1,1,8,9,5,3,
%U A385809 7,1,8,6,8,7,7,9,9,1,6,3,3,0,9,4,9,4,9,0,7,4,2,0,3,0,8,2,8,1,3,9,7,5,4,1,9,9,5,5,0,8
%N A385809 Decimal expansion of the Product_{p prime} (p^3-1)/(p^3+1).
%C A385809 Product_{p prime} (p^(2*n)-1)/(p^(2*n)+1) are rational numbers A114362(n)/A114363(n) = zeta(4*n)/zeta(2*n)^2.
%C A385809 Product_{p prime} (p^(2*n+1)-1)/(p^(2*n+1)+1) = zeta(2*(2*n+1))/zeta(2*n+1)^2.
%H A385809 Richard Mathar, <a href="https://arxiv.org/abs/0903.2514">Hardy-Littlewood Constants Embedded into Infinite Products over All Positive Integers</a>, arXiv:0903.2514 [math.NT], 2009-2011, Table 1 p. 2.
%F A385809 Equals zeta(6)/zeta(3)^2.
%F A385809 Equals 1 / A376742. - _Amiram Eldar_, Aug 01 2025
%e A385809 0.70407248732078447829629819997862445809258378...
%t A385809 RealDigits[Zeta[6]/Zeta[3]^2,10,105][[1]]
%o A385809 (PARI) prodeulerrat((p^3-1)/(p^3+1))
%Y A385809 Cf. A002117, A013664, A112407, A114362, A114363, A376742.
%K A385809 nonn,cons,changed
%O A385809 0,1
%A A385809 _Artur Jasinski_, Aug 01 2025
%E A385809 a(109) corrected by _Georg Fischer_, Aug 31 2025