The totient sum function has an identity:

$\displaystyle\sum_{k=1}^{N}\varphi(k) = \sum_{k=1}^N {\rm M}(\lfloor\frac{N}{k}\rfloor)k $

$\varphi(k)$ is the Euler totient function, and $M$ is the Mertens function $\displaystyle M(N)=\sum_{k=1}^N \mu (k)$ where $\mu$ is the Moebius function.

My question: What is the Mertens function summation equivalent of $\displaystyle\sum_{k=1}^{N}k\varphi(k) $ and $\displaystyle\sum_{k=1}^{N}k^2\varphi(k)$?