Product of Factors of Perfect Number

Theorem
Let $P$ be the perfect number $2^{n - 1} \paren {2^n - 1}$.

Then:
 * $\displaystyle \prod_{d \mathop \divides P} d = P^n$

Proof
The factors of $P$ are:
 * $1, 2, 4, \dots, 2^{n - 1}, 2^n - 1, 2 \paren {2^n - 1}, \dots, 2^{n - 1} \paren {2^n - 1}$

Therefore their product is: