Question 16
Let $n \geq 2$ be a natural number. Let $d_{1}, \ldots, d_{r}$ be all the distinct positive divisors of $n$ that are smaller than $n$ itself. Determine all $n$ for which:
$$
\operatorname{lcm}\left(d_{1}, \ldots, d_{r}\right) \neq n
$$
$$
\operatorname{lcm}\left(d_{1}, \ldots, d_{r}\right) \neq n
$$