Factors and Function

You are given two natural number $A$ and $B$ . Let $C$ be their product i.e. $C = A\times B$. Lets say $C$ has n factors (not necessarily prime factors) $a_1,a_2,a_3,a_4,a_5...a_n$ . Also ,lets define a function $F(x)$ such that $F(x)=p_1 \times q_1+p_2 \times q_2+p_3 \times q_3 +.....p_m \times q_m$ where prime factorisation of $x$ is $x$=$p_1$$q_1$$\times $$p_2$$q_2$$\times$ $p_3$$q_3$$\times $