2013 AMC 10B Problem 24

A positive integer n is *nice* if there is a positive integer m with exactly four positive divisors (including 1 and m) such that the sum of the four divisors is equal to n. How many numbers in the set \{ 2010,2011,2012,\ldots,2019 \} are nice?

\textbf{(A)}\ 1 \qquad\textbf{(B)}\ 2 \qquad\textbf{(C)}\ 3 \qquad\textbf{(D)}\ 4 \qquad\textbf{(E)}\ 5

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