Colored beads on a loop

Question

Suppose we have $p$ beads of $n$ different colors on a loop. $p$ is a prime number and we consider the loop to be the same if one is a rotation of the other. Then how many distinct beads are there? By using Burnside's Lemma, I have the result of $\frac{(p-1)n+n^p}{p}$, but not quite sure about my reasoning. (There are $(p-1)$ rotations of order $p$, each stabilizes $n$ colorings; there is 1 rotation of order 1, which stabilizes $n^p$ colorings).