洛谷 P2398 GCD SUM

https://www.luogu.com.cn/problem/P2398

\[\sum_{i = 1}^n \sum_{j = 1}^n \gcd(i, j) = \sum_{i = 1}^n \sum_{j = 1}^n \sum_{d \mid \gcd(i, j)} \varphi(d) = \sum_{d = 1}^n \varphi(d)\left\lfloor\frac{n}{d}\right\rfloor^2 \]

线性筛筛出 \(\varphi\) 即可。