Multiple of Perfect Number is Abundant

Theorem
Let $n$ be a perfect number.

Let $m$ be a positive integer such that $m > 1$.

Then $m n$ is abundant.

Proof
We have by definition of $\sigma$ function and perfect number that:
 * $\dfrac {\sigma \left({n}\right)} n = 2$

But from Abundancy Index of Product is greater than Abundancy Index of Proper Factors:
 * $\dfrac {\sigma \left({m n}\right)} {m n} > 2$

Hence the result by definition of abundant.