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%I #26 Feb 04 2024 03:24:07
%S 1,2,3,1,2,9,1,1,4,8,8,8,8,6,0,3,5,6,2,7,7,4,7,8,7,6,5,1,2,7,2,0,3,3,
%T 7,0,9,8,6,3,6,9,4,5,9,4,5,6,1,7,1,5,3,4,1,2,4,8,3,1,1,2,8,7,5,6,9,2,
%U 6,9,6,0,7,9,7,4,1,0,8,6,7,8,0,7,2,2,1,1,4,0,4,9,3,3,5,2,7,8,2
%N Decimal expansion of Product_{p prime} (1 + 1/(p*(p^2-1))).
%H G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a> [Cached copy]
%F Equals Sum_{k>=1} 1/A001615(A036966(k)). - _Amiram Eldar_, Jun 23 2020
%F Equals Sum_{k>=1} A003557(k)/k^3. - _Amiram Eldar_, Jan 25 2024
%F Equals lim_{m->oo} (1/m) * Sum_{k=1..m} A047994(k)/A000010(k). - _Amiram Eldar_, Feb 04 2024
%e 1.2312911488886035627747876512720337...
%t $MaxExtraPrecision = 600; digits = 99; terms = 600; P[n_] := PrimeZetaP[n]; LR = Join[{0, 0, 0}, LinearRecurrence[{0, 2, -1, -1, 1}, {3, 0, 5, -3, 7}, 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*(p^2-1))) \\ _Amiram Eldar_, Mar 17 2021
%Y Cf. A000010, A001615, A003557, A036966, A047994, A072802.
%K cons,nonn
%O 1,2
%A _N. J. A. Sloane_, Nov 19 2001
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