## 5-smooth totients

### Problem 516

5-smooth numbers are numbers whose largest prime factor doesn't exceed 5.

5-smooth numbers are also called Hamming numbers.

Let S(L) be the sum of the numbers n not exceeding L such that Euler's totient function φ(n) is a Hamming number.

S(100)=3728.

Find S(10^{12}). Give your answer modulo 2^{32}.