Is there a name for $\sum\left\lfloor\frac{n}{p^i}\right\rfloor$

Question

Is there a name for this function? $$f(n,p)=\sum_{i=1}^\infty\left\lfloor\frac{n}{p^i}\right\rfloor, \quad n,p\in \mathbb{N}$$ It's left unnamed in the OEIS, Wolfram Alpha doesn't recognise it, but it's a common theme in some Project Euler problems and it seems important.

Answer 1

This is the $p$-adic valuation of $n!$, that is the largest number $m$ with $p^m\mid n!$.