Abundancy

Author

Eric W. Weisstein
June 30, 2005

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

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

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

Code

Abundancy[n_Integer?Positive]:=DivisorSigma[1,n]/n
SetAttributes[Abundancy,Listable]

Enumeration

Timing[Take[a=Abundancy[Range[10^5]],100]]

<<Utilities`Plot`

IntegerListPlot[Take[a,200]]

ListPlot[Take[a,{1,10^5,10^1}],PlotJoined->True,PlotStyle->Red,PlotRange->All]

Through[{Numerator,Denominator}[Take[a,20]]]

Integer Ratios

Position[a,_Integer]//Flatten

Abundancy[%]