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

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

Offset

1,3

Links

Table of n, a(n) for n=1..10.

Formula

Lim_{n->oo} a(n)/10^n = 0.00869419399... (A318645) is the density of e-perfect numbers.

Example

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

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

Crossrefs

Cf. A051377, A054979, A318645, A307821.

Sequence in context: A225314 A200767 A222513 * A225613 A358982 A243922

Adjacent sequences: A307819 A307820 A307821 * A307823 A307824 A307825

Keyword

nonn,more

Author

Amiram Eldar, Apr 30 2019

Status

approved