AMC 12 2004a Problem 25

For each integer $n\geq 4$, let $a_n$ denote the base-$n$ number $0.\overline{133}_n$. The product $a_4a_5...a_{99}$ can be expressed as $\frac {m}{n!}$, where $m$ and $n$ are positive integers and $n$ is as small as possible. What is the value of $m$?

$\text {(A) } 98 \text {(B) } 101 \text {(C) } 132 \text {(D) } 798 \text {(E) }962$