莫反推式子trick

• $ \varphi (ij)=\frac{\varphi (i)\varphi (j)}{\varphi (gcd(i,j))}*gcd(i,j)$

• $ \mu (ij)=\mu (i) \mu(j)[gcd(i,j)=1]$

• $ d(ij)=\sum_{d_{1}|i}\sum_{d_{2}|i}[gcd(d_{1},d_{2})=1] $

• $ \sum_{1}^{n} A_{i}[d|A_{i}] \sum_{1}^{n} A_{j}[d|A_{j}] = ( \sum_{1}^{n} A_{i}[d|A_{i}])^{2} $