cp's OEIS Frontend

A380602 Decimal expansion of the asymptotic mean of the ratio A000005(k)/A322483(k).

%I A380602 #5 Jan 28 2025 01:48:59
%S A380602 1,2,3,5,8,7,9,7,7,7,5,2,6,1,7,3,5,4,8,7,1,0,9,3,8,0,5,3,1,8,9,4,5,1,
%T A380602 1,0,4,4,7,7,5,2,7,5,0,3,7,0,3,0,5,4,8,6,3,8,6,2,9,3,6,8,6,8,4,7,1,1,
%U A380602 0,0,2,2,9,1,4,5,9,3,3,4,8,6,7,0,3,7,8,3,8,5,6,5,2,3,6,6,0,9,4,4,9,6,9,1,7
%N A380602 Decimal expansion of the asymptotic mean of the ratio A000005(k)/A322483(k).
%F A380602 Equals lim_{m->oo} (1/m) * Sum_{k=1..m} A000005(k)/A322483(k).
%F A380602 Equals Product_{p prime} (2*p - (1+p-2*p^2)*log(1-1/p^2)*p).
%e A380602 1.23587977752617354871093805318945110447752750370305...
%t A380602 $MaxExtraPrecision = 1000; m = 1000; f[x_] := 2/x - (1 + 1/x - 2/x^2)*Log[1-x^2]/x; c = Rest[CoefficientList[Series[Log[f[x]], {x, 0, m}], x]]; RealDigits[Exp[NSum[Indexed[c, k]*PrimeZetaP[k], {k, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 120][[1]]
%o A380602 (PARI) default(realprecision, 120); default(parisize, 30000000);
%o A380602 my(m = 1024, x = 'x + O('x^m), v); v = Vec(2/x - (1 + 1/x - 2/x^2)*log(1-x^2)/x); prodeulerrat(sum(i=1, #v, v[i]/p^(i-1)))
%Y A380602 Cf. A000005, A322483, A380601 (mean of the inverse ratio).
%Y A380602 Similar constants: A307869, A361059, A361061.
%K A380602 nonn,cons
%O A380602 1,2
%A A380602 _Amiram Eldar_, Jan 27 2025