KöMaL 2015 B4698

Give an example for sets $H_1,H_2,\ldots\subset\mathbb{N}$ for which the following conditions hold: $a)$ $|H_n|=n$ for all positive integers $n$ . $b)$ For all positive integers $n$ and $k$ , $H_n \cap H_k = H_{(n,k)}$, where $(n,k)$ is the greatest common divisor of $n$ and $k$ .