[seqfan] Re: Reference that "A027687 4-perfect numbers" is finite

[Georgi Guninski]

Thank you.

Asked because an odd perfect number and infinitely mersenne primes implies
4-perfect numbers are infinite (and a lot of other 2k-perfect numbers) -
take the product of the OPN and coprime to it EPN.

On the other hand 4-perfect being finite and infinitely mersenne primes
implies no OPN.

What is the reason to believe all 4-perfect are discovered (even if they
are finite)?


On Mon, Jul 16, 2012 at 01:42:51PM +0400, Max Alekseyev wrote:
> I suspect that finiteness of A027687 is not proved but "extremly
> probable" as stated at Achim Flammenkamp's page:
> http://wwwhomes.uni-bielefeld.de/achim/mpn.html
> (notice the difference between answers "yes and proved" and simply
> "yes" in the column "Are all discovered?").
> 
> The flag 'fini' is thus inappropriate.
> 
> Max
> 
> On Sun, Jul 15, 2012 at 6:31 PM, Georgi Guninski <guninski at guninski.com> wrote:
> > What is the reference that A027687 is finite?
> >
> > Some searches show this as conjecture for k>=3.
> >
> > Any reference for k-perfect numbers, k>=4 will do.
> >
> > Thanks.
> >
> >
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