Multiple of Abundant Number is Abundant

Theorem
Let $n$ be an abundant 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 abundant number that:
 * $\sigma \left({n}\right) > 2 n$

Each of the divisors of $n$ can be multiplied by $m$, and these numbers will all be divisors of $m n$.

Thus:
 * $\sigma \left({m n}\right) \ge 2 m n$

Hence the result by definition of abundant.