5-smooth totients

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(10¹²). Give your answer modulo 2³².

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