Working on a problem I encounter the following sum:

$\sum_{r<R}\frac{\mu(r)^{2}\tau_{k}(r)^{2}}{\varphi(r)}$ that I have to estimate on the above; here $\tau_{k}(r)$ is the number of ways of writing $r$ as a product of $k$ natural integers. I now that $\sum_{r<R}\tau_{k}(r)=RP_{k-1}(R)+E(R)$ with $P_{k-1}(x)$ a polynomial of degree $k-1$ with leading coefficient $\frac{1}{k!}$ and $E(R)$ the error term.

Can anyone help me to obtain the desired estimate?