Euler's $\phi$ function: Find all $n$ such that $\phi(n)=n/3$

Question

I need help finding all $n$ such that $\phi(n)=n/3$.

I understand how to do it for $n/2$ but not for $n/3$. Thank you.

Answer 1

Write $n=3^am$ with $3\nmid m$. Now $$\phi(n)=2\cdot 3^{a-1}\phi(m)$$ so you get $$\phi(m)=\frac{m}{2},$$ which you say you know how to solve.