I have a simple question regarding a particular form of a sum and I was hoping someone could provide some insights or guidance.
if $n\:=\:\sum _{k=1}^n\frac{g\left(n,k\right)}{f\left(g\left(n,k\right)\right)}\:$
What are the properties of $f(x,y)$, $g(x,y),$ and most importantly, $n$? Bear in mind that in this particular sum, $x | f(x,y)$ and $x | g(x,y)$ Thank you in advance!