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The number of nonunitary abundant numbers below 10^n.
5

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

%S 0,5,75,812,8079,81052,808477,8097357,80939927,809350234

%N The number of nonunitary abundant numbers below 10^n.

%F Conjecture: Lim_{n->oo} a(n)/10^n = 0.0809... is the density of nonunitary abundant numbers.

%e Below 10^2 there are 5 nonunitary abundant numbers, 36, 48, 72, 80, and 96, thus a(2) = 5.

%t usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); nusigma[n_] := DivisorSigma[1, n] - usigma[n]; c = 0; k = 1; seq={}; Do[ While[ k < 10^n, If[ nusigma[k]>k, c++ ]; k ++]; AppendTo[seq, c], {n, 1, 5}]; seq

%Y Cf. A048146, A064597, A302992, A302993, A302994, A307820, A307821.

%K nonn,more

%O 1,2

%A _Amiram Eldar_, Apr 30 2019