Divisor Sum of Non-Square Semiprime

Theorem
Let $n \in \Z_{>0}$ be a semiprime with distinct prime factors $p$ and $q$.

Then:
 * $\sigma \left({n}\right) = \left({p + 1}\right) \left({q + 1}\right)$

where $\sigma \left({n}\right)$ denotes the sigma function.

Proof
As $p$ and $q$ are distinct prime numbers, it follows that $p$ and $q$ are coprime.

Thus by Sigma Function is Multiplicative:
 * $\sigma \left({n}\right) = \sigma \left({p}\right) \sigma \left({q}\right)$

From Sigma of Prime Number:
 * $\sigma \left({p}\right) = \left({p + 1}\right)$
 * $\sigma \left({q}\right) = \left({q + 1}\right)$

Hence the result.