$\left[\frac n1\right]+ \left[\frac n2\right] + \cdots+\left[\frac nn\right]+\left[\sqrt n\right]$ is even
How to show that $\lfloor n/1\rfloor+\lfloor n/2 \rfloor+....+\lfloor n/n\rfloor+\lfloor{\sqrt{n}}\rfloor$ is even?