Divisor Counting Function from Prime Decomposition/Proof 2

Proof
From Divisor Counting Function of Power of Prime we have:
 * $\forall j \in \closedint 1 r: \map {\sigma_0} {p_j^{k_j} } = k_j + 1$

The result follows immediately from Divisor Counting Function is Multiplicative‎.