## Multiples with small digits

### Problem 303

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, $\sum \limits_{n = 1}^{100} {\dfrac{f(n)}{n}} = 11363107$.

Find $\sum \limits_{n=1}^{10000} {\dfrac{f(n)}{n}}$.