A361059 - OEIS

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A361059

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

1, 1, 5, 8, 8, 5, 4, 5, 7, 2, 6, 5, 0, 3, 1, 2, 1, 0, 0, 1, 6, 4, 4, 8, 0, 1, 9, 6, 3, 9, 3, 1, 7, 5, 1, 4, 9, 0, 3, 9, 1, 0, 4, 3, 1, 8, 8, 5, 7, 3, 9, 5, 9, 6, 3, 4, 5, 2, 6, 1, 0, 6, 1, 5, 1, 4, 8, 2, 3, 3, 7, 9, 7, 4, 9, 3, 5, 4, 6, 4, 9, 0, 6, 6, 6, 5, 1, 3, 9, 2, 1, 7, 9, 2, 9, 5, 4, 7, 3, 9, 6, 2, 5, 7, 3

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Biunitary Divisor.

FORMULA

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

Equals Product_{p prime} (1 - (p-1)*log(1 - 1/p^2)/(2*p)).

EXAMPLE

1.158854572650312100164480196393175149039104318857395...

MATHEMATICA

$MaxExtraPrecision = 1000; m = 1000; f[p_] := 1 - (p - 1)*Log[1 - 1/p^2]/(2*p); 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, 106][[1]]

CROSSREFS

Cf. A000005, A286324, A361060 (mean of the inverse ratio).

Cf. A307869 (unitary analog), A308043.

Sequence in context: A153611 A068470 A069997 * A199373 A247037 A265274

Adjacent sequences: A361056 A361057 A361058 * A361060 A361061 A361062

KEYWORD

nonn,cons

AUTHOR

Amiram Eldar, Mar 01 2023

STATUS

approved