A327839 Decimal expansion of the asymptotic density of numbers whose number of divisors is a power of 2 (A036537).

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

Offset: 0

Author

Amiram Eldar, Sep 27 2019

Keywords

• nonn
• cons

Examples

			0.687827139443624881063510824549870983203095875301015...
		

Links

• Vladimir Shevelev, S-exponential numbers, Acta Arithmetica, Vol. 175, No. 4 (2016), pp. 385-395, alternative link.

Crossrefs

Cf. A036537, A036538.

Programs

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]]

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.