Mock AIME 6 2006-2007 Problems/Problem 14

Problem

A rational $\frac{1}{k}$ , where $k$ is a positive integer, is said to be $\textit{n-unsound}$ if its base $N$ representation terminates. Let $S_n$ be the set of all $\textit{n-unsound}$ rationals. The sum of all the elements in the union set $S_2\cup S_3\cup\cdots\cup S_{14}$ is $\frac mn$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .

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Mock AIME 6 2006-2007 Problems/Problem 14

Problem

Solution