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.

A361060 Decimal expansion of the asymptotic mean of A286324(k)/A000005(k), the ratio between the number of bi-unitary divisors and the number of divisors.

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%I A361060 #6 Feb 16 2025 08:34:04
%S A361060 9,0,1,2,4,1,8,0,6,8,2,6,4,8,2,2,5,5,1,3,9,1,9,7,4,8,5,0,9,4,3,8,7,5,
%T A361060 5,8,9,8,2,8,1,1,5,3,3,8,2,1,7,8,7,6,2,8,7,6,2,6,1,6,1,2,0,6,3,0,9,0,
%U A361060 7,3,4,3,7,3,3,1,8,6,0,8,3,7,9,3,6,3,5,5,9,5,4,0,8,6,0,1,0,5,2,4,5,6,4,9,8
%N A361060 Decimal expansion of the asymptotic mean of A286324(k)/A000005(k), the ratio between the number of bi-unitary divisors and the number of divisors.
%H A361060 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BiunitaryDivisor.html">Biunitary Divisor</a>.
%F A361060 Equals lim_{m->oo} (1/m) * Sum_{k=1..m} A286324(k)/A000005(k).
%F A361060 Equals Product_{p prime} (2 - 1/p - (p-1)*log((p+1)/(p-1))/2).
%e A361060 0.901241806826482255139197485094387558982811533821787...
%t A361060 $MaxExtraPrecision = 1000; m = 1000; f[p_] := 2 - 1/p - (p - 1)*Log[(p + 1)/(p - 1)]/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 A361060 Cf. A000005, A286324, A361059 (mean of the inverse ratio).
%Y A361060 Cf. A307869, A308043 (unitary analog).
%K A361060 nonn,cons
%O A361060 0,1
%A A361060 _Amiram Eldar_, Mar 01 2023