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 $\le 2$.
Thus $f(2)=2$, $f(3)=12$, $f(7)=21$, $f(42)=210$, $f(89)=1121222$.
Also, $\sum \limits_{n = 1}^{100} {\dfrac{f(n)}{n} } = 11363107$.
Find $\sum \limits_{n=1}^{10000} {\dfrac{f(n)}{n} }$.