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%I #13 Mar 13 2021 10:04:42
%S 9,4,7,7,3,3,2,6,2,1,4,3,6,7,5,3,7,5,9,3,9,5,2,1,5,3,7,6,5,4,1,8,9,6,
%T 1,3,0,3,3,6,3,1,6,3,2,3,1,7,4,1,3,8,5,2,8,2,8,7,5,1,0,8,8,9,0,9,3,2,
%U 3,3,2,9,4,7,8,9,8,9,9,8,7,1,3,9,5,3,4,4,1,2,8,2,6,1,3,4,4,9
%N Decimal expansion of Product_{p prime} (1 - 1/(p^3*(p+1))).
%H G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a>. [Cached copy]
%e 0.947733262143675375939521537654189613...
%t $MaxExtraPrecision = 600; digits = 98; terms = 600; P[n_] := PrimeZetaP[n]; LR = Join[{0, 0, 0, 0}, LinearRecurrence[{-2, -1, 0, 1, 1}, {-4, 5, -6, 7, -12}, 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^3*(p+1))) \\ _Amiram Eldar_, Mar 13 2021
%Y Cf. A078085.
%K cons,nonn
%O 0,1
%A _N. J. A. Sloane_, Nov 19 2001
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