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A327837 Decimal expansion of the asymptotic mean of the number of exponential divisors function (A049419). 1
1, 6, 0, 2, 3, 1, 7, 1, 0, 2, 3, 0, 5, 4, 1, 8, 0, 5, 2, 3, 4, 9, 6, 2, 6, 3, 1, 5, 6, 2, 1, 1, 6, 1, 0, 0, 3, 7, 7, 6, 9, 3, 9, 4, 9, 5, 7, 8, 5, 5, 7, 2, 7, 3, 7, 7, 4, 6, 5, 3, 5, 2, 8, 5, 9, 8, 7, 8, 8, 8, 8, 6, 0, 2, 1, 6, 3, 3, 5, 4, 7, 2, 7, 5, 6, 6, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..87.

Abdelhakim Smati and Jie Wu, On the exponential divisor function, Publications de l'Institut Mathématique, Vol. 61 (1997), pp. 21-32.

László Tóth, An order result for the exponential divisor function, Publ. Math. Debrecen, Vol. 71, No. 1-2 (2007), pp. 165-171, arXiv preprint,, arXiv:0708.3552 [math.NT], 2007.

Jie Wu, Problème de diviseurs exponentiels et entiers exponentiellement sans facteur carré, Journal de théorie des nombres de Bordeaux, Vol. 7, No. 1, (1995), pp. 133-141.

FORMULA

Equals lim_{k->oo} A145353(k)/k.

Equals Product_{p prime} (1 + Sum_{e >= 2} p^(-e) * (d(e) - d(e-1))), where d(e) is the number of divisors of e (A000005).

EXAMPLE

1.602317102305418052349626315621161003776939495785572...

MATHEMATICA

$MaxExtraPrecision = 1500; m = 1500; em = 500; f[x_] := 1 + Log[1 + Sum[x^e * (DivisorSigma[0, e] - DivisorSigma[0, e - 1]), {e, 2, em}]]; c = Rest[ CoefficientList[Series[f[x], {x, 0, m}], x] * Range[0, m] ]; RealDigits[ Exp[NSum[Indexed[c, k] * PrimeZetaP[k]/k, {k, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]]

CROSSREFS

Cf. A000005, A049419, A145353.

Cf. A059956 (constant for unitary divisors), A306071 (bi-unitary), A327576 (infinitary).

Sequence in context: A129106 A070062 A274542 * A261166 A021170 A329093

Adjacent sequences:  A327834 A327835 A327836 * A327838 A327839 A327840

KEYWORD

nonn,cons

AUTHOR

Amiram Eldar, Sep 27 2019

STATUS

approved

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Last modified July 10 14:17 EDT 2020. Contains 335576 sequences. (Running on oeis4.)