login
The number of e-perfect numbers below 10^n.
2

%I #6 May 07 2019 15:19:07

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

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

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

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

%t 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

%Y Cf. A051377, A054979, A318645, A307821.

%K nonn,more

%O 1,3

%A _Amiram Eldar_, Apr 30 2019