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%I #13 Mar 13 2021 10:04:46
%S 9,7,5,8,2,4,1,5,3,0,4,7,6,6,8,2,4,1,6,7,9,0,1,1,4,3,6,5,9,4,7,9,9,8,
%T 3,1,9,7,1,7,6,4,9,7,1,2,2,9,2,1,2,6,0,9,4,4,2,5,1,5,7,7,3,2,4,4,2,0,
%U 6,2,6,7,0,6,8,5,8,3,6,0,8,3,6,6,5,4,6,1,8,5,6,3,6,8,5,7,3,1
%N Decimal expansion of Product_{p prime} (1 - 1/(p^4*(p+1))).
%H G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a>. [Cached copy]
%e 0.97582415304766824167901143659479983...
%t $MaxExtraPrecision = 500; digits = 98; terms = 500; P[n_] := PrimeZetaP[n]; LR = Join[{0, 0, 0, 0, 0}, LinearRecurrence[{-2, -1, 0, 0, 1, 1}, {-5, 6, -7, 8, -9, 5}, 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^4*(p+1))) \\ _Amiram Eldar_, Mar 13 2021
%Y Cf. A078084.
%K cons,nonn
%O 0,1
%A _N. J. A. Sloane_, Nov 19 2001