Multiples with small digits

Published on Saturday, 25th September 2010, 10:00 pm; Solved by 3016;
Difficulty rating: 35%

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