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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 $a+b+c$?

 Feb 1, 2021
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From the product formula, the product works out to n^((n + 3)/2), so a + b + c = 1 + 3 + 2 = 6.

 Feb 1, 2021

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