TR-MO 2019 Problem 6

Given an integer $n>2$ and an integer $a$ , if there exists an integer $d$ such that $n\mid a^d-1$ and $n\nmid a^{d-1}+\cdots+1$ , we say $a$ is $n-$ separating. Given any n>2, let the defect of $n$ be defined as the number of integers $a$ such that $0<a<n$ , $(a,n)=1$ , and $a$ is not $n-$ separating. Determine all integers $n>2$ whose defect is equal to the smallest possible value.