RO-NMO 2014 Problem 101

Let be a natural number $n.$ Calculate $$\sum_{k=1}^{n^2}\#\left\{ d\in\mathbb{N}| 1\le d\le k\le d^2\le n^2\wedge k\equiv 0\pmod d \right\} .$$ Here, $\#$ means cardinal.