A327576 Decimal expansion of the constant that appears in the asymptotic formula for average order of the number of infinitary divisors function (A037445).

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, section 1.7.5, pp. 53-54.

Links

Table of n, a(n) for n=0..86.

Graeme L. Cohen and Peter Hagis, Jr., Arithmetic functions associated with infinitary divisors of an integer, International Journal of Mathematics and Mathematical Sciences, Vol. 16, No. 2 (1993), pp. 373-383.

Formula

Equals Limit_{n->oo} A327573(n)/(2 * n * log(n)). [Corrected by Amiram Eldar, May 07 2021]

Equals (1/2) * Product_{P} (1 - 1/(P+1)^2), where P are numbers of the form p^(2^k) where p is prime and k >= 0 (A050376).

Example

0.366625276945381909556532720687001563033612155971009...

Mathematica

m = 1000; em = 10; f[x_] := Sum[Log[1 - 1/(1 + 1/x^(2^e))^2], {e, 0, em}]; c = Rest[CoefficientList[Series[f[x], {x, 0, m}], x]*Range[0, m]]; $MaxExtraPrecision = 1500; RealDigits[(1/2)*Exp[f[1/2] + f[1/3]]* Exp[NSum[Indexed[c, k]*(PrimeZetaP[k] - (1/2)^k - (1/3)^k)/k, {k, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]]

Crossrefs

Cf. A037445, A050376, A327573.

Cf. A059956 (corresponding constant for unitary divisors), A306071 (bi-unitary).

Sequence in context: A187601 A113737 A292165 * A331058 A040006 A358548

Adjacent sequences: A327573 A327574 A327575 * A327577 A327578 A327579

Keyword

nonn,cons

Author

Amiram Eldar, Sep 17 2019

Status

approved