Perfect numbers

A number is said to be perfect if it is equal to the sum of its proper divisors.
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)(2p-1) with 2p-1 prime

Number 2p-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...

 

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