cp's OEIS Frontend

A383057 Decimal expansion of the asymptotic mean of A056671(k)/A034444(k), the ratio between the number of squarefree unitary divisors and the number of unitary divisors over the positive integers.

%I A383057 #6 Apr 15 2025 10:26:12
%S A383057 7,8,9,3,6,2,6,0,1,2,6,0,9,8,9,0,2,9,1,0,3,7,0,8,6,2,9,2,5,1,3,9,6,8,
%T A383057 9,2,7,6,8,5,1,6,7,6,0,5,2,6,9,1,6,5,0,5,3,3,3,6,8,4,7,4,1,6,1,3,6,0,
%U A383057 9,9,3,9,8,8,2,2,5,2,7,5,3,6,3,2,5,0,2,0,3,4,3,4,4,8,7,0,9,9,0,8,4,9,1,1,4
%N A383057 Decimal expansion of the asymptotic mean of A056671(k)/A034444(k), the ratio between the number of squarefree unitary divisors and the number of unitary divisors over the positive integers.
%C A383057 The asymptotic mean of the inverse ratio A034444(k)/A056671(k) is 15/Pi^2 (A082020).
%F A383057 Equals lim_{m->oo} (1/m) * Sum_{k=1..m} A056671(k)/A034444(k).
%F A383057 Equals Product_{p prime} (1 - 1/(2*p^2)).
%e A383057 0.78936260126098902910370862925139689276851676052691...
%t A383057 $MaxExtraPrecision = 300; m = 300; f[p_] := 1 - 1/(2*p^2); c = Rest[CoefficientList[Series[Log[f[1/x]], {x, 0, m}], x]]; RealDigits[Exp[NSum[Indexed[c, n]*(PrimeZetaP[n]), {n, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 120][[1]]
%o A383057 (PARI) prodeulerrat(1 - 1/(2*p^2))
%Y A383057 The unitary analog of A308043.
%Y A383057 Cf. A034444, A056671, A082020, A383058.
%K A383057 nonn,cons
%O A383057 0,1
%A A383057 _Amiram Eldar_, Apr 15 2025