OBM 2020 Problem 1

Prove que existem inteiros positivos $a_1, a_2, \ldots, a_{2020}$ tais que

$$\frac{1}{a_1} + \frac{1}{2a_2} + \frac{1}{3a_3} + \cdots + \frac{1}{2020a_{2020}} = 1.$$