Sum of prime factors with multiplicity ($s(n)={\sum }_{j=1}^r{e}_j{p}_j$)

For an integer $n>1$ with prime factorization $n={\prod }_{j=1}^r{p}_j^{e_j}$, this is the sum of its prime factors with each repeated $e_j$ times. For example, $s(18)=2+3+3=8$. It differs from the sum of distinct prime factors.