Why is this code better than the functional approach? Note that it saves an enormous amount of time since this approach does not need to scan through all the integers! It are simply a few calculations (at which a computer is good at). All the code (the naive approach and the better approach) can be found on GitHub.
Having a solid understanding of mathematics and logic can help you come up with superior algorithms, but make sure you comment them in detail so that the next dev (who might not understand the underpinnings of your code) doesn’t replace it with a brute-force method because it’s “easier.”