18 Let $n$ be a given positive integer. Find all positive integers $m$, such that there exist positive integers $x_{1}<x_{2}<\cdots<x_{n}$, satisfying: $\frac{1}{x_{1}}+\frac{2}{x_{2}}+\cdots+\frac{n}{x_{n}}=m$.
18. Let $m$ be a positive integer that meets the requirement, i.e., there exist positive integers $x_{1}<x_{2}<\cdots<x_{n}$, such that
$$\frac{1}{x_{1}}+\frac{2}{x_{2}}+\cdots+\frac{n}{x_{n}}=m$$

Then
$$x_{i} \geqslant i(1 \leqslant i \leqslant n)$$

Hence
$$\frac{i}{x_{i}} \leqslant 1,1 \leqslant i \leqslant n$$

Thus $\square$
$$m \leqslant n$$

Next, we prove: For any positive integer $m$, if $1 \leqslant m \leqslant n$, then there exist $x_{1}, x_{2}, \cdots, x_{n}$ that satisfy (1). When $m=n$, take $x_{i}=i$;
When $m=1$, take $x_{i}=n \cdot i$;
When $1<m<n$, take $x_{1}=1, x_{2}=2, \cdots, x_{n-1}=m-1, x_{m}=(n-m+1) m, x_{m+1}=(n-m+1)(m+1), \cdots, x_{n}=(n-m+1) \cdot n$.

Therefore, the $m$ that satisfies the condition is $1,2, \cdots, n$.