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Problem 625

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Gcd sum

$G(N)=\sum _{j=1}^N\sum _{i=1}^j\text{gcd}(i,j)$.
You are given: $G(10)=122$.

Find $G({10}^{11})$. Give your answer modulo 998244353.

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最大公约数之和

令$G(N)=\sum _{j=1}^N\sum _{i=1}^j\text{gcd}(i,j)$。
已知$G(10)=122$。

求$G({10}^{11})$，并将你的答案对998244353取模。

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