A Moebius sum

Abstract

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