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perfect square divisors of 13!

Source: 2023 AIME I #4

February 8, 2023

AMCAIMEAIME I

Problem Statement

The sum of all positive integers

m

for which

\tfrac{13!}{m}

is a perfect square can be written as

2^{a}3^{b}5^{c}7^{d}11^{e}13^{f}

, where

a, b, c, d, e,

and

f

are positive integers. Find

a+b+c+d+e+f

.

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