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A341748 Decimal expansion of zeta(3) * Product_{p prime} (1 - 3/p^2 + 2/p^3 - 1/p^4 + 2/p^5 - 1/p^6).

%I A341748 #5 Feb 19 2021 09:46:35
%S A341748 3,3,0,9,1,8,2,9,6,2,0,8,5,0,8,8,6,5,9,7,7,0,8,9,9,7,9,9,1,3,2,2,7,8,
%T A341748 5,4,8,9,3,5,4,3,3,4,5,4,1,0,4,8,9,4,2,7,0,5,4,3,6,0,1,4,1,8,8,5,5,4,
%U A341748 2,4,4,1,4,1,6,5,8,7,8,3,5,2,6,0,0,0,1
%N A341748 Decimal expansion of zeta(3) * Product_{p prime} (1 - 3/p^2 + 2/p^3 - 1/p^4 + 2/p^5 - 1/p^6).
%C A341748 The constant c in the asymptotic formulas Sum_{n1, n2 <= x} phi(lcm(n1, n2)) = c * x^4/4 + O(x^(7/2 + eps)) and Sum_{n1, n2 <= x} phi(lcm(n1, n2))/(n1*n2) = c * x^2 + O(x^(3/2 + eps)).
%H A341748 Titus Hilberdink and László Tóth, <a href="https://doi.org/10.1016/j.jnt.2016.05.024">On the average value of the least common multiple of k positive integers</a>, Journal of Number Theory, Vol. 169 (2016), pp. 327-341. See p. 333.
%e A341748 0.33091829620850886597708997991322785489354334541048...
%t A341748 $MaxExtraPrecision = 1500; m = 1500; c = LinearRecurrence[{-1, 2, 0, 1, -1}, {0, -6, 6, -22, 40}, m]; f[x_] := 1 - 3 x^2 + 2 x^3 - x^4 + 2 x^5 - x^6; Zeta[3] * f[1/2] * f[1/3] * Exp[NSum[Indexed[c, n]*(PrimeZetaP[n] - 1/2^n - 1/3^n)/n, {n, 2, m}, NSumTerms -> m, WorkingPrecision -> m]]
%o A341748 (PARI) zeta(3) * prodeulerrat(1 - 3/p^2 + 2/p^3 - 1/p^4 + 2/p^5 - 1/p^6)
%Y A341748 Cf. A000010 (phi), A240976, A341747.
%K A341748 nonn,cons
%O A341748 0,1
%A A341748 _Amiram Eldar_, Feb 18 2021