A307823 The number of nonunitary abundant numbers below 10^n.

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

Offset: 1

Author

Amiram Eldar, Apr 30 2019

Keywords

• nonn
• more

Examples

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

Crossrefs

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

Programs

Mathematica

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

Formula

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