I'm trying to express the following function more simply:
\begin{equation*} f(x) = (\sum_{n=3}^{x} \prod_{k=2}^{\lceil \sqrt n \rceil} \lceil \dfrac {n}{k} \rceil - \lfloor \dfrac{n}{k} \rfloor ) + 1 . \end{equation*}
I know this is kind of a vague request, but I'm trying to get away from the ceiling and floor functions and possibly the product notation, just because it feels like a hacky way of expressing what I'm trying to express.
Any ideas?