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Ore's conjecture

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Revision as of 22:12, 2 May 2009 by Vipul (talk | contribs) (Created page with '==Statement== The conjecture states that the harmonic mean of all the positive divisors of an odd natural number greater than <math>1</math> cannot be an integer. ==Related...')

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Statement

The conjecture states that the harmonic mean of all the positive divisors of an odd natural number greater than $1$ cannot be an integer.

Related facts and conjectures

Weaker conjectures

Odd perfect number conjecture: The harmonic mean of the divisors of a perfect number is an integer, hence Ore's conjecture implies that there does not exist any odd perfect number.

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