14. 24 * Find all positive integers $n$ such that all integers not exceeding $\sqrt{n}$ divide $n$.

Find all positive integers $n$ such that all integers not exceeding $\sqrt{n}$ divide $n$.
Let $x=[\sqrt{n}]$. Suppose $x \geqslant 3 . x-1$ and $x, x-2$ are coprime, and the greatest common divisor of $x$ and $x-2$ is 2 or 1. The required $n$ is divisible by $x-1, x, x-2$, so $n \geqslant \frac{(x-1) x(x-2)}{2}, 2 n \geqslant (\sqrt{n}-1)(\sqrt{n}-2)(\sqrt{n}-3)=n \sqrt{n}-6 n+11 \sqrt{n}-6$. Therefore, $8 \geqslant \sqrt{n}, n \leqslant 64$. By checking all positive integers not exceeding 64, we get $n=24,12,8,6,4,2$.