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 A065469 #21 Jan 14 2022 07:32:00 %S A065469 5,3,0,7,1,1,8,2,0,4,7,2,0,4,4,7,9,4,9,7,2,9,4,3,7,7,2,4,7,2,9,7,7,1, %T A065469 7,0,9,4,7,8,6,1,0,2,2,2,0,9,8,6,0,4,0,3,4,7,5,8,1,9,0,4,9,2,8,0,9,0, %U A065469 5,0,6,7,9,2,6,0,9,5,7,9,0,6,3,8,6,3,8,1,9,2,4,5,6,3,6,2,3,5 %N A065469 Decimal expansion of Product_{p prime} (1 - 1/(p^2-1)). %H A065469 G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a>. [Cached copy] %F A065469 Product of A013661 by A065474. - _R. J. Mathar_, Mar 26 2011 %F A065469 From _Amiram Eldar_, Jan 14 2022: (Start) %F A065469 Equals Sum_{k>=1} mu(k)/(phi(k)*sigma(k)), where mu is the Möbius function (A008683), phi is the Euler totient function (A000010) and sigma(k) is the sum of divisors of k (A000203). %F A065469 Equals Sum_{k>=1} mu(k)/J_2(k), where J_2 is Jordan's totient function (A007434). (End) %e A065469 0.53071182047204479497294377247... %t A065469 $MaxExtraPrecision = 800; digits = 98; terms = 800; P[n_] := PrimeZetaP[n]; LR = LinearRecurrence[{0, 3, 0, -2}, {0, 0, -2, 0}, terms + 10]; r[n_Integer] := LR[[n]]; Exp[NSum[r[n]*P[n - 1]/(n - 1), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits + 10]] // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Apr 18 2016 *) %o A065469 (PARI) prodeulerrat(1 - 1/(p^2-1)) \\ _Amiram Eldar_, Mar 13 2021 %Y A065469 Cf. A000010, A000203, A007434, A008683, A013661, A065474, A072101. %K A065469 cons,nonn %O A065469 0,1 %A A065469 _N. J. A. Sloane_, Nov 19 2001