Divisor Sum of Non-Square Semiprime/Proof 1

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

Thus by Divisor Sum Function is Multiplicative:
 * $\map {\sigma_1} n = \map {\sigma_1} p \map {\sigma_1} q$

From Sigma Function of Prime Number:
 * $\map {\sigma_1} p = \paren {p + 1}$
 * $\map {\sigma_1} q = \paren {q + 1}$

Hence the result.