A Moebius sum

We provide numerical bounds for $\mathrm{\Sigma }(X)={\sum }_{\begin{array}{c}{d}_1,d_2\le X\end{array}}\frac{\mu (d_1)\mu (d_2)}{[d_1,d_2]}$. We show in particular that $0\le \mathrm{\Sigma }(X)\le 17\mathrm{/}25$ for every $X\ge 2$.