A361060 - OEIS

%I #5 Mar 01 2023 02:39:34

%S 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 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 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BiunitaryDivisor.html">Biunitary Divisor</a>.

%F Equals lim_{m->oo} (1/m) * Sum_{k=1..m} A286324(k)/A000005(k).

%F Equals Product_{p prime} (2 - 1/p - (p-1)*log((p+1)/(p-1))/2).

%e 0.901241806826482255139197485094387558982811533821787...

%t $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 Cf. A000005, A286324, A361059 (mean of the inverse ratio).

%Y Cf. A307869, A308043 (unitary analog).

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Mar 01 2023