2006 Cayley Problem 22

A positive integer is called *multiplicatively perfect* if it is equal to the product of its proper divisors. For example, 10 is multiplicatively perfect since its proper divisors are 1, 2 and 5, and it is true that 1 \times 2 \times 5 = 10. How many multiplicatively perfect integers are there between 2 and 30?

\textbf{(A)}\ 9\quad \textbf{(B)}\ 5\quad \textbf{(C)}\ 8\quad \textbf{(D)}\ 6\quad \textbf{(E)}\ 4

If there are no answer choices shown, enter a numerical answer.

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