2005 AMC 10A Problem 21

For how many positive integers n does 1+2+\cdots+n evenly divide 6n?

\textbf{(A) } 3\qquad \textbf{(B) } 5\qquad \textbf{(C) } 7\qquad \textbf{(D) } 9\qquad \textbf{(E) } 11

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