## The totient of a square is a cube

### Problem 342

Published on Saturday, 11th June 2011, 01:00 pm; Solved by 507; Difficulty rating: 50%
Consider the number 50.

50^{2} = 2500 = 2^{2} × 5^{4}, so φ(2500) = 2 × 4 × 5^{3} = 8 × 5^{3} = 2^{3} × 5^{3}. ^{1}

So 2500 is a square and φ(2500) is a cube.

Find the sum of all numbers n, 1 < n < 10^{10} such that φ(n^{2}) is a cube.

^{1} φ denotes **Euler's totient function**.