8. (i) Let $N=9450$, find $\varphi(N)$.
(ii) Find the sum of all positive integers not greater than 9450 and coprime with 9450.
8. (i) Solution: Given $9450=2 \cdot 3^{3} \cdot 5^{2} \cdot 7$, and by Lemma 14, we have
$$\begin{aligned}
\varphi(N) & =9450\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{5}\right)\left(1-\frac{1}{7}\right) \\
& =\frac{2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 2 \cdot 4 \cdot 6}{2 \cdot 3 \cdot 5 \cdot 7}=2160
\end{aligned}$$
(ii) Solution: Let the sum of all positive integers not greater than 9450 and coprime with 9450 be $S$. By Problem 5, we have
$$\begin{aligned}
S & =\frac{1}{2} \cdot 9450 \cdot \varphi(9450) \\
& =\frac{1}{2} \times 9450 \times 2160 \\
& =10206000
\end{aligned}$$