Only Partially Perfect?

A multiplicative perfect number is a positive integer \(n\) who's divisors' product totals to \(n^2\).

For example, the factors of \(22\) are \(1,2,11,22,~~1\cdot2\cdot11\cdot22=484\)

Define the term partially-multiplicative perfect number as a positive integer who's divisor's product totals to \(n^{\frac{5}{2}}\). Find the sum of the first 4 partially-multiplicative perfect numbers.

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