[seqfan] Re: Should this be cited as a link to A000396?

Richard Guy rkg at cpsc.ucalgary.ca
Thu Feb 10 17:23:07 CET 2011

There is some inconsistency in usage in the literature.  It is
not always agreed that 1 is a proper divisor.  For  n > 1,  a
possible solution is to define the ``aliqout parts'' of  n  to
be the divsors of  n  apart from  n  itself, so that a perfect
number is equal to the sum of its aliquot parts.  I'm not sure
what to do about  n = 1.  It seems certain that  sigma(1) = 1,
which gives  s(n) = sigma(n) - n  to be  0  when  n = 1.  This
would make it quite clear to us aliquot sequence pursuers when
a sequence had terminated.       R.

On Wed, 9 Feb 2011, Jonathan Post wrote:

> A000396  Perfect numbers n: n is equal to the sum of the proper divisors of n.
> Note on the Theory of Perfect Numbers
> Authors: N. A. Carella
> (Submitted on 8 Feb 2011)
> http://arxiv.org/abs/1102.1885
> A perfect number is a number whose divisors add up to twice the number
> itself. The existence of odd perfect numbers is a millennia-old
> unsolved problem. This note proposes a proof of the nonexistence of
> odd perfect numbers. More generally, the same analysis seems to
> generalize to a proof of the nonexistence of odd multiperfect numbers.
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