The totient of a square is a cube
Problem 342
Published on Saturday, 11th June 2011, 01:00 pm; Solved by 427
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.