Find the smallest positive integer $n$ such that if $n = p_1^{a_1} p_2^{a_2} \ldots p_s^{a_s}$, then \[ \phi(n) = n \left(1 - \frac{1}{p_1}\right) \left(1 - \frac{1}{p_2}\right) \ldots \left(1 - \frac{1}{p_s}\right) = \frac{2^5}{47}n. \]

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