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The product of the proper positive integer factors of $n$ can be written as $n^{(ax+b)/c}$, where $x$ is the number of positive divisors $n$ has, $c$ is a positive integer, and the greatest common factor of the three integers $a$, $b$, and $c$ is $1$. What is $a+b+c$?

 Dec 25, 2020
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By the product formula, the product of proper divisors of n is n^((3x + 3)/2), so a + b + c = 3 + 3 + 2 = 8.

 Jan 3, 2021

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