(25 points) (1) First, select $n$ numbers from $1,2, \cdots, 2020$, then choose any two numbers $a$ and $b$ from these $n$ numbers, such that $a \nmid b$. Find the maximum value of $n$.


Sure, here is the translated text:

```
(1) Notice that any two numbers in $A_{k}$ have a divisibility relationship. Therefore, at most one number can be taken from each array, which means a maximum of 1010 numbers can be taken.

Also, taking the numbers $1011, 1012, \cdots, 2020$ (1010 numbers) meets the requirement, so $n_{\max }=1010$.
```

This translation preserves the original format and structure of the text.