Ore's Conjecture

Author

Eric W. Weisstein
October 13, 2004

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

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

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

Initialization

HarmonicMeanOfDivisors[n_]:=DivisorSigma[0,n]/Plus@@(1/Divisors[n])

Enumeration

h=HarmonicMeanOfDivisors/@Range[10]

Through[{Numerator,Denominator}[h]]

Conjecture

Position[HarmonicMeanOfDivisors/@Range[1,10^5,2],_IntegerQ]//Timing