Robin's Theorem

Author

Eric W. Weisstein
February 9, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PrimeNumbers/RobinsTheorem.nb.

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

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

Inequality

<<Utilities`Plot`
<<Utilities`Typesetting`

IntegerListPlot[Table[Exp[EulerGamma]n Log[Log[n]]-DivisorSigma[1,n],{n,2,200}],AxesLabel->TraditionalForm/@{n,Exp[EulerGamma]n Log[Log[n]]-DivisorSigma[1,n]}]

Position[Table[DivisorSigma[1,n]<Exp[EulerGamma]n Log[Log[n]],{n,100}],True]//Flatten

Position[Table[DivisorSigma[1,n]<Exp[EulerGamma]n Log[Log[n]],{n,10000}],False]//Flatten//Timing