2019 AMC 12A Problem 13

How many ways are there to paint each of the integers 2, 3, \ldots, 9 either red, green, or blue so that each number has a different color from each of its proper divisors?

\textbf{(A)}\ 144\qquad\textbf{(B)}\ 216\qquad\textbf{(C)}\ 256\qquad\textbf{(D)}\ 384\qquad\textbf{(E)}\ 432

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