%I #15 Sep 02 2022 04:56:55
%S 0,0,1,12,102,1045,10449,104365,1043641,10436775,104367354
%N The number of exponential abundant numbers below 10^n.
%F 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]
%e Below 10^3 there is only one exponential abundant number, A129575(1) = 900, thus a(3) = 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, A129575, A302992, A302993, A302994, A307820, A307822, A307823.
%K nonn,more
%O 1,4
%A _Amiram Eldar_, Apr 30 2019
%E a(11) from _Amiram Eldar_, Sep 02 2022