Will factorization work?

$123456789 =p_1^{q_1} \cdot p_2^{q_2} \cdot p_3^{q_3} \cdots p_n^{q_n}$ Let $p_1, p_2, \ldots , p_n$ be distinct prime numbers satisfying the equation above, and $q_1, q_2, \ldots, q_n$ be positive integers.

Find $p_1 +p_2 + \cdots + p_n$ .