# Why Only Semi-Perfect

Number Theory Level 5

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 semi-multiplicative perfect number as a positive integer who's divisors' product (including the number itself) totals to $$n^3$$. Find the sum of the first 8 semi-multiplicative perfect numbers.

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