Counting Conundrum

Geometry Level 3

How many real $x$ satisfying $0 \leq x \leq 2017$ are there such that $x \sin(\pi x)$ is an integer?

Bonus: Can you come up with a simple formula for how many $0 \leq x \leq n$ there are such that $x \sin(\pi x)$ is an integer, where $n$ is a positive integer?