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Divisor Square Sum

Problem 211

Published on Saturday, 4th October 2008, 02:00 am; Solved by 2312

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.