For a positive integer $k$, let $d(k)$ denote the number of divisors of $k$, and let $s(k)$ denote the digit sum of $k$. A positive integer $n$ is said to be amusing if there exists a positive integer $k$ such that $d(k) = s(k) = n$. What is the smallest amusing odd integer greater than 1?

Let's think step by step and output the final answer within \boxed{}.
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