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