Abundant Number

Author

Eric W. Weisstein
May 20, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/NumberTheory/AbundantNumber.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/AbundantNumber.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Table

Select[Range[99],AbundantQ]//Timing

Length[%]

Select[Range[1,9999,2],AbundantQ]

Density Function

s=DivisorSigma[1,Range[10000]];//Timing

counts=Table[Count[Take[s,n],_?(#≥2n&)]/n,{n,5000}];//Timing

ListPlot[counts,Joined->True,PlotStyle->Red,AxesLabel->{n,(Subscript[A, n])[2]}]

counts[[-1]]//N