Bounding a phi-function summation Is there anyway to bound the values that are taken on by the following sum:
$$\frac{\sum _{k \in \mathbb{Z}_n} \sum _{d |k} d \varphi \left( \frac{n}{d} \right)}{n^3}$$
(Disclaimer: NOT ALL terms in the summation exist, but when the fraction $\frac{n}{d}$ is not an integer, set that term equal to $0$) 
I tried to work with the fact that each term in the summation will contribute a $\varphi(n)$, and then using results from bounding the term $\varphi(n)/n$ from other MSE posts, but that really didn't resolve the problem. Could someone please shed some light onto this problem?

So you meant $$\frac1{n^3}\sum_{k=1}^n \sum_{d| \gcd(n,k)} d \varphi(n/d) =\frac1{n^3}\sum_{d | n} d \varphi(n/d) \sum_{k=1, d | k}^n 1= \ldots$$
