(Kind of bash) According to the problem, $47(p_1-1)(p_2-1)\ldots(p_s-1)=2^5p_1p_2\ldots{p_s}$. Therefore, among $p_1~p_s$ there must be at least one that is $47$, so we can assume $p_1=47$. $46\prod_{i=2}^s(p_i-1)=2^5\prod_{i=2}^sp_i$, so $23\prod_{i=2}^s(p_i-1)=2^4\prod_{i=2}^sp_i$. Assume that $p_2=23$, then $11\prod_{i=3}^s(p_i-1)=2^3\prod_{i=3}^sp_i$. Assume that $p_3=11$, then $5\prod_{i=4}^s(p_i-1)=2^2\prod_{i=4}^sp_i$. Assume that $p_4=5$, then $\prod_{i=5}^s(p_i-1)=\prod_{i=5}^sp_i$. Therefore, the smallest n is $47\times23\times11\times5$ which is $59455$.