%I #10 Feb 28 2023 07:46:22

%S 2,9,6,0,0,8,0,3,0,2,0,2,4,9,4,1,4,1,0,4,8,1,8,2,0,4,7,8,1,1,0,8,9,4,

%T 6,9,3,9,2,8,4,3,9,0,9,5,9,2,5,1,6,3,4,1,1,9,6,7,5,0,4,4,8,0,8,6,6,3,

%U 3,9,3,5,7,8,7,3,7,3,8,2,4,9,5,8,4,6,2,6,7,3,8,5,0,1,0,8,0,5,1,7,8,6,0,6,6

%N Decimal expansion of a constant related to the asymptotics of A361012.

%F Equals limit_{n->oo} A361012(n) / n.

%F Equals Product_{p prime} (1 + Sum_{e>=2} (sigma(e) - sigma(e-1)) / p^e), where sigma = A000203.

%e 2.960080302024941410481820478110894693928439095925163411967504480866339...

%t $MaxExtraPrecision = 1000; smax = 500; Do[Clear[f]; f[p_] := 1 + Sum[(DivisorSigma[1, e] - DivisorSigma[1, e-1])/p^e, {e, 2, emax}]; cc = Rest[CoefficientList[Series[Log[f[1/x]], {x, 0, smax}], x, smax + 1]]; Print[f[2] * f[3] * f[5] * f[7] * Exp[N[Sum[cc[[n]]*(PrimeZetaP[n] - 1/2^n - 1/3^n - 1/5^n - 1/7^n), {n, 2, smax}], 120]]], {emax, 100, 1000, 100}]

%Y Cf. A361012, A327837, A327838.

%K nonn,cons

%O 1,1

%A _Vaclav Kotesovec_, Feb 28 2023