pefect numbers

[Antreas P. Hatzipolakis]

>to reply to a recent posting:  it is believed that there are
>no odd prefect numbers.  it is known that all even perfect numbers
>are of the form 2^n(2^(n+1)-1) where 2^(n+1)-1 is prime [Hardy and Wright
>p 239]
>njas

2^(n+1)-1: prime ==> 2^n(2^(n+1) - 1) : perfect  (EUCLID)

N: even perfect ==> N is of Euclid type (EULER)

So, A000396's:
Formula:   The numbers 2^(p-1)(2^p - 1) are perfect, where p is a prime such
           that 2^p- 1 is also prime (see A000043, the Mersenne primes), and
           it is believed that there are no other perfect numbers.

would be more precise if written:

Formula:   The numbers 2^(p-1)(2^p - 1) are perfect, where p is a prime such
           that 2^p- 1 is also prime (see A000043, the Mersenne primes).
           There are no other even perfect numbers, and it is believed
           that there are no odd perfect numbers.


APH