[seqfan] Re: number theory question about A000593

[Max Alekseyev]

Basically this conjecture is equivalent to whether there exists an odd
number m such that (sigma(m)-1)/m equals 2^k for some integer k>0.

I do not know even if there exists an integer m such that
(sigma(m)-1)/m is integer greater than 1 (equivalently, sigma(m) == 1
(mod m) and sigma(m)>m+1).

Max

On Sat, Jun 18, 2011 at 7:37 PM, Peter Lawrence
<peterl95124 at sbcglobal.net> wrote:
>
> I was tinkering with A000593 "sum of odd divisors of N" and noticed that
> empirically
>
> A(n)  =  n+1    IFF    isprime(n)                      <--- conjecture ???
>
>
> (a bit of finagling results in only needing to check for odd squares, so a
> simple C program
> verifies this out to 10^12 pretty fast)
>
>
> So I am wondering if this is actually true, and if so is there is any N.T.
> proof.
>
>
>
> apologies in advance if this is too off-topic for this list,
> thanks,
> Peter Lawrence.
>
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