If $n=p_1^{a_1},p_2^{a_2}...p_s^{a_s}$ then $\phi (n)=n \left(1- \frac{1}{p_1}\right)\left(1 - \frac{1}{p_2}\right)...\left(1- \frac{1}{p_s}\right)$. Find the smallest positive integer $n$ such that $\phi (n)=\frac{2^5}{47}n.$
Source: China Northern MO 2015 grade 10 p3 CNMO
Tags: number theory, prime factorization
If $n=p_1^{a_1},p_2^{a_2}...p_s^{a_s}$ then $\phi (n)=n \left(1- \frac{1}{p_1}\right)\left(1 - \frac{1}{p_2}\right)...\left(1- \frac{1}{p_s}\right)$. Find the smallest positive integer $n$ such that $\phi (n)=\frac{2^5}{47}n.$