Problem 211

Divisor Square Sum

For a positive integer n, let σ₂(n) be the sum of the squares of its divisors. For example,

σ₂(10) = 1 + 4 + 25 + 100 = 130.

Find the sum of all n, 0 < n < 64,000,000 such that σ₂(n) is a perfect square.

约数平方和

对于正整数n，记σ₂(n)为其所有约数的平方和。例如，

σ₂(10) = 1 + 4 + 25 + 100 = 130.

在0 < n < 64,000,000中，有些n满足σ₂(n)为完全平方数，求所有这些n的和。