## The totient of a square is a cube

### Problem 342

Published on 11 June 2011 at 01:00 pm [Server Time]

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.