Divisor Square Sum

For a positive integer $n$ , let $σ_{2} (n)$ be the sum of the squares of its divisors. For example, $σ_{2} (10) = 1 + 4 + 25 + 100 = 130.$

Find the sum of all $n$ , $0 < n < 64 000 000$ such that $σ_{2} (n)$ is a perfect square.

Write-up coming later

The complete problem is available here. An approach, code, and answer will be added later.