# 303 : 小さい桁を持つ倍数

正の整数$$n$$に対し$$f(n)$$を、$$n$$の倍数であり 10 進数で表すと 2 以下の数字のみが用いられる最小の数と定義する。

すると$$f(2)=2, f(3)=12, f(7)=21, f(42)=210, f(89)=1121222$$である。

また$$\displaystyle \sum\_{n=1}^{100}\frac{f(n)}{n} = 11363107$$である。

$$\displaystyle \sum\_{n=1}^{10000} \frac{f(n)}{n}$$を求めよ。


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