A307821 The number of exponential abundant numbers below 10^n.

0, 0, 1, 12, 102, 1045, 10449, 104365, 1043641, 10436775, 104367354

Offset: 1

Author

Amiram Eldar, Apr 30 2019

Keywords

• nonn
• more

Examples

			Below 10^3 there is only one exponential abundant number, A129575(1) = 900, thus a(3) = 1.
		

Crossrefs

Cf. A051377, A129575, A302992, A302993, A302994, A307820, A307822, A307823.

Programs

Mathematica

fun[p_, e_] := DivisorSum[e, p^# &]; esigma[1] = 1; esigma[n_] := Times @@ fun @@@ FactorInteger[n]; c = 0; k = 1; seq={}; Do[ While[ k < 10^n, If[ esigma[k]>2k, c++ ]; k ++]; AppendTo[seq, c], {n, 1, 5}]; seq

Formula

Limit_{n->oo} a(n)/10^n = 0.001043673... is the density of exponential abundant numbers (see A129575). [Updated by Amiram Eldar, Sep 02 2022]

Extensions

a(11) from Amiram Eldar, Sep 02 2022