Very cool! There's definitely some similarity to Ramanujan Sums, though the approach here sort of packages the fizz-buzz divisibility properties into one function.
https://en.wikipedia.org/wiki/Ramanujan%27s_sum
I can recommend the book Guide to Graph Colouring: Algorithms and Applications by Lewis. It covers techniques including some state of the art methods for getting good but not provably optimal colorings. It discusses in depth local search and hybrid evolutionary algorithms, which tend to be the best performing on academic benchmarks (DIMACS graphs and large random graphs).
Penn State has a bunch of their graduate stats courses online [1]. I worked through some of their time series class [2] and found it to be pretty good quality.
There are some closely related difficult problems. Consider the fraction a/b, and let r be the length of the repeating fractional part. Then r <= b - 1. Moreover, if r == b - 1, then b is prime. In general, r divides phi(b), where phi is the Euler phi function.
I've solved 249 of them. I don't remember when I joined, but it must have been about 10 years ago. Solving PE problems was a great way to unwind in grad school (studying math) and learn some cool math in the process. There was a period where I was knocking them out pretty frequently, but I've only had the time to solve 4 problems in the past year.
This a very terse proof. It is stated "The same method can also be used to prove that e cannot be a root of a second degree equation with rational coefficients", but if I recall correctly, the generalization for the irrationality of $e^2$ isn't entirely straightforward, mainly due to the presence of powers of 2 in the terms of the expansion.