# [seqfan] Re: Pairs Occurring Only Once Among # Of Divisors

Leroy Quet q1qq2qqq3qqqq at yahoo.com
Wed Jun 10 20:08:40 CEST 2009

```If by "k-th prime power", you mean p^k, for p = some prime, then it is possible for m+1 to equal something that is NOT a power of a prime in order for d(m+1) to = k+1, where k = prime. Did I understand your argument?

Either way, I don't think it has been proved that the number of Mersenne primes is infinite, or has it by now?

Leroy

--- On Wed, 6/10/09, Hagen von EItzen <math at von-eitzen.de> wrote:

> From: Hagen von EItzen <math at von-eitzen.de>
> Subject: [seqfan]    Pairs Occurring Only Once Among # Of Divisors
> To: seqfan at list.seqfan.eu
> Date: Wednesday, June 10, 2009, 5:36 PM
> If  n = 2^k - 1 is prime, then d(n)=2, d(n+1)=k+1.
> If d(m)=2 and d(m+1)=k+1, then m is prime and m+1 is a k-th
> prime power;
> if k>1, m must be odd, hence m+1=2^k.
> Thus A161460 contains at least all Mersenne primes
>
> Hagen
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

```