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 \text{ is a composite positive integer}\} ?

\begin{array}{l} \textbf{(A)}\; \text{the set of positive integers} \\ \textbf{(B)}\; \text{the set of composite positive integers} \\ \textbf{(C)}\; \text{the set of even positive integers} \\ \textbf{(D)}\; \text{the set of integers greater than 3} \\ \textbf{(E)}\; \text{the set of integers greater than 4} \end{array}

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