2015 AMC 12B Problem 18

For every composite positive integer $n$, define $r(n)$ to be the sum of the factors in the prime factorization of $n$. For example, $r(50) = 12$ because the prime factorization of $50$ is $2 \times 5^2$, and $2 + 5 + 5 = 12$. What is the range of the function $r$, $\{r(n): n$ is a composite positive integer$\}$ ?

$\mathrm{(A) \ } \text{the set of positive integers} \qquad \mathrm{(B) \text{the set of composite positive integers} \ } \qquad \mathrm{(C) \text{the set of even positive integers}}\qquad \mathrm{(D) \text{the set of integers greater than 3}} \qquad \mathrm{(E) \text{the set of integers greater than 4}}$

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.