For instance 6=1+2+3, 28=1+2+4+7+14

All the known perfect numbers are even and given by the formula :

2^{(p-1)}(2^{p}-1) with 2^{p}-1 prime |

Number 2^{p}-1 is not prime for every p.

It is a prime (Mersenne prime) for p=2, 3, 5, 7, 13, 17, 19, 31...

Other problems and relations about divisors :

Multiperfect numbers, amicable numbers, aliquot sequences...