HMMT 2014 T2

Let $a_{1}, a_{2}, \ldots$ be an infinite sequence of integers such that $a_{i}$ divides $a_{i+1}$ for all $i \geq 1$, and let $b_{i}$ be the remainder when $a_{i}$ is divided by 210 . What is the maximal number of distinct terms in the sequence $b_{1}, b_{2}, \ldots$ ?