Problem 342
The totient of a square is a cube
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.
平方数的总计函数为立方数
考虑数50。
502 = 2500 = 22 × 54，因此φ(2500) = 2 × 4 × 53 = 8 × 53 = 23 × 53。1
所以2500是一个平方数，而φ(2500)是一个立方数。
有些数1 < n < 1010满足φ(n2)为立方数，求所有这类数的和。
1 φ表示欧拉总计函数。