6. Find all positive integers $n$ that satisfy the following equations:
(i) $\varphi(n)=\varphi(2 n)$;
(ii) $\varphi(2 n)=\varphi(3 n)$;
(iii) $\varphi(3 n)=\varphi(4 n)$.
6. (i) $2 \nmid n$; (ii) $2 \mid n, 3 \nmid n$; (iii) $2 \nmid n, 3 \nmid n$. In (ii), (iii) only discuss
$$n=2^{a} 3^{\beta} \cdot m, \quad(6, m)=1$$