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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.
3
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, 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, 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
OFFSET
0,1
LINKS
Eric Weisstein's World of Mathematics, Biunitary Divisor.
FORMULA
Equals lim_{m->oo} (1/m) * Sum_{k=1..m} A286324(k)/A000005(k).
Equals Product_{p prime} (2 - 1/p - (p-1)*log((p+1)/(p-1))/2).
EXAMPLE
0.901241806826482255139197485094387558982811533821787...
MATHEMATICA
$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]]
CROSSREFS
Cf. A000005, A286324, A361059 (mean of the inverse ratio).
Cf. A307869, A308043 (unitary analog).
Sequence in context: A158336 A021530 A110909 * A364830 A345738 A197070
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Mar 01 2023
STATUS
approved