For a positive integer $n$, let $\sigma_2(n)$ be the sum of the squares of its divisors. For example, $$\sigma_2(10) = 1 + 4 + 25 + 100 = 130.$$
Find the sum of all $n$, $0 \lt n \lt 64\,000\,000$ such that $\sigma_2(n)$ is a perfect square.
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