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The totient of a square is a cube

Problem 342

Published on Saturday, 11th June 2011, 01:00 pm; Solved by 483

Consider the number 50.
502 = 2500 = 22 × 54, so φ(2500) = 2 × 4 × 53 = 8 × 53 = 23 × 53. 1
So 2500 is a square and φ(2500) is a cube.

Find the sum of all numbers n, 1 < n < 1010 such that φ(n2) is a cube.

1 φ denotes Euler's totient function.