A302993 Number of unitary abundant numbers < 10^n.
0, 5, 64, 691, 7011, 70030, 699597, 7005450, 70048740, 700321813, 7003128054, 70034216605, 700350142296, 7003426996800, 70033987968599, 700341098675985, 7003416399263312
Offset: 1
Programs
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Mathematica
usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; uabQ[n_] := usigma[n] > 2 n; c = 0; k = 1; seq={}; Do[While[k < 10^n, If[uabQ[k], c++]; k++]; AppendTo[seq, c], {n, 1, 5}]; seq
Formula
Conjecture: Lim_{n->oo} a(n)/10^n = 0.07... is the density of unitary abundant numbers.
Extensions
a(10)-a(17) from Hiroaki Yamanouchi, Aug 03 2018