TITLE: If $n = 18k+5$ is composite, there are at least 9 divisors of $\phi(n)$ which do not divide $n-1$
QUESTION [6 upvotes]: If $n$ is a composite of the form $18k+5$, there at least 9 divisors of $\phi(n)$ which do not divide $n-1$. Is this true in general or if not, what is the smallest counter example? The conjecture has been verified for $n \le 1 \times 10^7$.
Related question.
Note: The question was posted in MSE a year ago but got no answer. Hence posting in MO

REPLY [3 votes]: Positive answer to this question would imply that there are no solutions to Lehmer's totient problem of the form $18k+5$. I'm not aware of known restrictions of this kind.