RU-ALLRUSSIAN 1981 Problem 10

The sequence $\mathbf{a}_{\mathrm{n}}$ of positive integers is such that (1) $\mathbf{a}_{\mathrm{n}} \leq \mathbf{n}^{3 / 2}$ for all n, and (2) m- n divides $\mathbf{k}_{\mathrm{m}} - \mathbf{k}_{\mathrm{n}}$ (for all $\mathbf{m} > \mathbf{n}$ ). Find $\mathbf{a}_{\mathrm{n}}$ .