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A327576 Decimal expansion of the constant that appears in the asymptotic formula for average order of the number of  infinitary divisors function (A037445). 3
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 (list; constant; graph; refs; listen; history; text; internal format)
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 A155067

Adjacent sequences:  A327573 A327574 A327575 * A327577 A327578 A327579

KEYWORD

nonn,cons

AUTHOR

Amiram Eldar, Sep 17 2019

STATUS

approved

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Last modified September 27 19:23 EDT 2021. Contains 347694 sequences. (Running on oeis4.)