Sum of Reciprocals of Divisors of Perfect Number is 2

Theorem
Let $n$ be a perfect number.

Then:
 * $\displaystyle \sum_{d \mathop \backslash n} \dfrac 1 d = 2$

That is, the sum of the reciprocals of the divisors of $n$ is equal to $2$.

Proof
The result follows by definition of perfect number: