Definition:Perfect Number

Definition
A perfect number is a (strictly) positive integer equal to the sum of all its divisors except itself.

Formally stated, a perfect number $n$ is a (strictly) positive integer such that:
 * $\sigma \left({n}\right) = 2 n$

where $\sigma: \Z_{>0} \to \Z_{>0}$ is the sigma function.

Also see

 * Definition:Abundance


 * Theorem of Even Perfect Numbers: An even perfect number is of the form $2^{n-1} \left({2^n - 1}\right)$, where $2^n - 1$ is prime.


 * Are All Perfect Numbers Even?