cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A361062 Decimal expansion of the asymptotic mean of A073184(k)/A000005(k), the ratio between the number of cubefree divisors and the number of divisors.

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%I A361062 #5 Mar 01 2023 02:39:50
%S A361062 9,3,9,9,7,4,3,5,2,1,7,6,4,7,7,0,7,8,4,7,0,4,4,2,5,6,2,3,8,6,0,2,5,7,
%T A361062 2,6,7,6,9,8,4,2,3,1,0,9,7,7,9,9,6,7,3,3,0,5,9,8,1,3,8,2,1,6,7,4,6,1,
%U A361062 3,5,9,5,5,2,0,4,4,8,0,1,3,5,9,2,5,3,1,3,0,3,8,4,8,1,0,5,1,2,9,4,6,6,6,7,1
%N A361062 Decimal expansion of the asymptotic mean of A073184(k)/A000005(k), the ratio between the number of cubefree divisors and the number of divisors.
%F A361062 Equals lim_{m->oo} (1/m) * Sum_{k=1..m} A073184(k)/A000005(k).
%F A361062 Equals Product_{p prime} (-(p-1)*(1+4*p+6*p^2*log(1-1/p))/(2*p^2)).
%e A361062 0.939974352176477078470442562386025726769842310977996...
%t A361062 $MaxExtraPrecision = 1000; m = 1000; f[p_] := -(p-1)*(1+4*p+6*p^2*Log[1-1/p])/(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, 100][[1]]
%Y A361062 Cf. A000005, A073184, A361061 (mean of the inverse ratio).
%Y A361062 Cf. A307869, A308043 (squarefree analog).
%K A361062 nonn,cons
%O A361062 0,1
%A A361062 _Amiram Eldar_, Mar 01 2023