摘要： $$ \sum_{a_{1}=1}^{n} \sum_{a_{2}=1}^{n} \ldots \sum_{a_{x}=1}^{n}\left(\prod_{j=1}^{x} a_{j}^{k}\right) f\left(\operatorname{gcd}\left(a_{1}, a_{2}, \ldots, a_{x}\right)\right) \cdot \operatorname{gcd}\left(a_{1}, a_{2}, \ldots, a_{x}\right) $$ 阅读全文