A307822 The number of e-perfect numbers below 10^n.

0, 1, 8, 87, 871, 8690, 86940, 869417, 8694205, 86941922, 869419437, 8694194033

Offset: 1

Author

Amiram Eldar, Apr 30 2019

Keywords

• nonn
• more

Examples

			Below 10^2 there is only one e-perfect number, A054979(1) = 36, thus a(2) = 1.
		

Crossrefs

Cf. A051377, A054979, A318645, A307821.

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 = 0.00869419399... (A318645) is the density of e-perfect numbers.

Extensions

a(11)-a(12) from Amiram Eldar, May 06 2025