The important fact that the sum of divisors number-theortic function is weakely multiplicative.
That is if then,
The prove is simple because,
Since is multiplicative so that is .
What is where ?
Since is odd and only have even divisors we have,
is a Mersenne prime thus,
That is a geometric series whose sum is,
(The converse that an even perfect number has this form is a little bit more complicated).