How can I evaluate ( estimate ) the sum $s(n)=\sum_{k=1}^{n-1}\mu ^{2}(k(n-k))$ ($\mu$ is  Mobius function) . Trivial estimate  
$s(n)<\varphi (n)$ follow from the fact that $\mu (k(n-k))$ is zero if $k$ is not prime to $n$. It seem that in the case of $n$ - primorial,  $s(n)$ is pretty close to $\varphi (n)$