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Problem 516

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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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5-光滑总计函数

5-光滑数是指最大质因数不超过5的数。

5-光滑数也被称为汉明数。

若数n不超过L，且欧拉总计函数φ(n)是汉明数，记所有这样的数之和为S(L)。

已知S(100)=3728。

求S(10¹²)，将其模2³²取余作为你的答案。

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