MathNet 2014 Question 57

Let $n\ge1$ be an integer. Determine all integers $p\ge1$ for which there exist positive integers $x_1\lt x_2\lt \cdots\lt x_n$ such that $$\frac1{x_1}+\frac2{x_2}+\cdots+\frac n{x_n}=p.$$