2020 Cayley Problem 25

How many positive integers n \le 20\,000 have the properties that 2n has 64 positive divisors including 1 and 2n, and 5n has 60 positive divisors including 1 and 5n?

\textbf{(A)}\ 4\quad \textbf{(B)}\ 5\quad \textbf{(C)}\ 3\quad \textbf{(D)}\ 2\quad \textbf{(E)}\ 6

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Full credit to this problem is given to the CEMC, you may view all Cayley contests here.