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A327839 Decimal expansion of the asymptotic density of numbers whose number of divisors is a power of 2 (A036537). 7
6, 8, 7, 8, 2, 7, 1, 3, 9, 4, 4, 3, 6, 2, 4, 8, 8, 1, 0, 6, 3, 5, 1, 0, 8, 2, 4, 5, 4, 9, 8, 7, 0, 9, 8, 3, 2, 0, 3, 0, 9, 5, 8, 7, 5, 3, 0, 1, 0, 1, 5, 2, 1, 7, 1, 0, 5, 6, 4, 0, 1, 6, 9, 0, 8, 8, 7, 4, 8, 4, 9, 1, 6, 4, 6, 2, 8, 2, 9, 6, 3, 5, 9, 4, 7, 0, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
Vladimir Shevelev, S-exponential numbers, Acta Arithmetica, Vol. 175, No. 4 (2016), pp. 385-395, alternative link.
FORMULA
Equals Product_{p prime} (1 - 1/p) * (1 + Sum_{i>=1} 1/p^(2^i-1)).
Equals lim_{k->oo} A036538(k)/2^k.
EXAMPLE
0.687827139443624881063510824549870983203095875301015...
MATHEMATICA
$MaxExtraPrecision = 1000; m = 1000; em = 10; f[x_] := Log[(1 - x)*(1 + Sum[x^(2^e - 1), {e, 1, 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
Sequence in context: A133748 A225037 A157852 * A365125 A088608 A323984
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Sep 27 2019
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)