of the sums $s(n,p)$ defined above. What is $\sum_{d|n}s(d,p)$? Let $r=\href{http://en.wikipedia.org/wiki/Radical_of_an_integer}{\text{rad}}\,n$ $=\prod_{q\mid n}q$ be the product of all primes $q$ dividing $n$ (also called the radical or squarefree kernel of $n$). What does it tell us when the positive (but not necessarily prime) integer $p$ is less than $\frac{n}r$? Or equal