https://www.luogu.com.cn/problem/P5221

莫比乌斯反演

\[\prod_{i=1}^N \prod_{j=1}^N \frac{lcm(i,j)}{\gcd(i,j)}\\ =\frac{\prod_{i=1}^N \prod_{j=1}^N ij}{\prod_{k=1}^N k^{(\sum_{p=1}^N \sum_{q=1}^N [\gcd(p,q)=k])}}\\ 处理\prod_{k=1}^N k^{(\sum_{p=1}^N \sum_{q=1}^N [\gcd(p,q)=k])} \]