Here is an interesting question that I thought of:
We call a subset $S$ of the positive integers good if for all $n \in S$, we have that $d \in S$ for all $d | n$. Find the number of good subsets of $\{1, 2, ..., n\}$.
If we let $f(n)$ be this number, we get $f(p) = 2f(p-1) - 1$ for primes $p$. But for non-prime $n$, it seems to difficult to connect it to earlier values of $n$.
Any solutions, suggestions, or comments would be appreciated