8. Let $g(n)=\sum_{k=1}^{n}(k, n)$, where $n \in \mathbf{N}^{*},(k, n)$ represents the greatest common divisor of $k$ and $n$, then the value of $g(100)$ is
答夏 520 .
解析 If $(m, n)=1$, then $g(m n)=g(m) g(n)$, so $g(100)=g(4) g(25)$. Also, $g(4)=1+2+1+4=8, g(25)=5 \times 4+25+(25-5)=65$, so $g(100)=8 \times 65=520$.