A383057 Decimal expansion of the asymptotic mean of A056671(k)/A034444(k), the ratio between the number of squarefree unitary divisors and the number of unitary divisors over the positive integers.

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

Offset

0,1

Comments

The asymptotic mean of the inverse ratio A034444(k)/A056671(k) is 15/Pi^2 (A082020).

Links

Table of n, a(n) for n=0..104.

Formula

Equals lim_{m->oo} (1/m) * Sum_{k=1..m} A056671(k)/A034444(k).

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

Example

0.78936260126098902910370862925139689276851676052691...

Mathematica

$MaxExtraPrecision = 300; m = 300; f[p_] := 1 - 1/(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, 120][[1]]

Prog

(PARI) prodeulerrat(1 - 1/(2*p^2))

Crossrefs

The unitary analog of A308043.

Cf. A034444, A056671, A082020, A383058.

Sequence in context: A198814 A254272 A284363 * A390975 A114514 A011471

Adjacent sequences: A383054 A383055 A383056 * A383058 A383059 A383060

Keyword

nonn,cons

Author

Amiram Eldar, Apr 15 2025

Status

approved