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%I #19 Jun 13 2021 05:16:37
%S 1,3,3,9,7,8,4,1,5,3,5,7,4,3,4,7,2,4,6,5,9,9,1,5,2,5,8,6,5,1,4,8,8,6,
%T 0,5,2,7,7,5,2,4,2,2,4,9,7,8,8,1,8,2,8,0,6,6,6,3,0,1,5,0,6,7,6,4,6,7,
%U 9,4,8,2,7,2,7,6,0,0,9,8,2,3,7,3,7,3,4,3,6,6,4,4,0,8,5,0,4,5,4
%N Decimal expansion of totient constant Product_{p prime} (1 + 1/(p^2*(p-1))).
%C The sum of the reciprocals of the cubefull numbers (A036966). - _Amiram Eldar_, Jun 23 2020
%H Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 86.
%H G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a> [Cached copy]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotientSummatoryFunction.html">Totient Summatory Function</a>
%F Equals (6/Pi^2) * A065484. - _Amiram Eldar_, Jun 23 2020
%e 1.339784153574347246599152586514886052775...
%t $MaxExtraPrecision = 500; digits = 99; terms = 500; P[n_] := PrimeZetaP[n]; LR = Join[{0, 0, 0}, LinearRecurrence[{2, -1, -1, 1}, {3, 4, 5, 3}, 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^2*(p-1))) \\ _Vaclav Kotesovec_, Sep 19 2020
%Y Cf. A036966, A065484, A078074.
%K cons,nonn
%O 1,2
%A _N. J. A. Sloane_, Nov 19 2001
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