P3327 [SDOI2015]约数个数和

\[d(ij)=\sum_{x|i}\sum_{y|j}[\gcd(x,y)=1]\\ \]

\[\sum_{i=1}^{n}\sum_{j=1}^{m}\sum_{x|i}\sum_{y|j}[\gcd(x,y)=1]\\ \sum_{x=1}^{n}\sum_{y=1}^{m}[\gcd(x,y)=1]\sum_{i=1}^{\frac nx}\sum_{j=1}^{\frac my}1\\ \sum_{x=1}^{n}\sum_{y=1}^{m}(\frac nx)(\frac my)\sum_{p|x,p|y}\mu(p)\\ \sum_{p=1}^{n} \mu(p) \sum_{x=1}^{\frac np}\sum_{y=1}^{\frac mp}(\frac n{xp})(\frac m{yp})\\ \]