2019 AMC 10A Problem 9

What is the greatest three-digit positive integer n for which the sum of the first n positive integers is \underline{\text{not}} a divisor of the product of the first n positive integers?

\textbf{(A) } 995 \qquad\textbf{(B) } 996 \qquad\textbf{(C) } 997 \qquad\textbf{(D) } 998 \qquad\textbf{(E) } 999

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