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%I #17 Jan 14 2022 07:32:25
%S 1,2,6,6,5,5,8,5,0,1,4,7,1,5,2,8,5,7,1,6,1,4,5,4,7,1,1,2,6,2,9,6,4,0,
%T 8,4,5,3,9,5,5,6,0,2,3,5,4,5,7,3,4,4,8,2,1,1,2,1,9,6,7,3,2,9,5,4,8,3,
%U 9,6,1,0,6,0,7,5,1,6,4,0,8,6,8,8,8,1,7,2,0,9,0,4,2,3,6,8,2,1,5
%N Decimal expansion of Product_{p prime} (1 + 1/(p+1)^2).
%H G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a>. [Cached copy]
%F Equals Sum_{k>=1} mu(k)^2/sigma(k)^2, where mu is the Möbius function (A008683) and sigma(k) is the sum of divisors of k (A000203). - _Amiram Eldar_, Jan 14 2022
%e 1.26655850147152857161454711262964...
%t $MaxExtraPrecision = 800; digits = 99; terms = 800; P[n_] := PrimeZetaP[n]; LR = LinearRecurrence[{-3, -4, -2}, {0, 0, 2}, 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 (PARI) prodeulerrat(1 + 1/(p+1)^2) \\ _Amiram Eldar_, Mar 15 2021
%Y Cf. A000203, A008683, A067009.
%K cons,nonn
%O 1,2
%A _N. J. A. Sloane_, Nov 19 2001
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