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Problem 303

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Multiples with small digits

For a positive integer n, define f(n) as the least positive multiple of n that, written in base 10, uses only digits ≤ 2.

Thus f(2)=2, f(3)=12, f(7)=21, f(42)=210, f(89)=1121222.

Also, $\sum _{n=1}^{100}\frac{f(n)}{n}=11363107$.

Find $\sum _{n=1}^{10000}\frac{f(n)}{n}$.

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数字较小的倍数

正整数n的有些正倍数在十进制下所有数字均≤ 2，记其中最小的为f(n)。

因此f(2)=2，f(3)=12，f(7)=21，f(42)=210，f(89)=1121222。

此外，已知$\sum _{n=1}^{100}\frac{f(n)}{n}=11363107$。

求$\sum _{n=1}^{10000}\frac{f(n)}{n}$。

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