Let $M$ be a positive integer with $M > 4$, and let $\varphi$ denote Euler's totient function. If a positive integer $n$ satisfies the Diophantine equation (*) $M \varphi(n) = n - 1$, then the number of prime factors of $n$ is much bigger than $M$. Moreover, the set of all squarefree integers which do not fulfil (*) contains ``nice'' subsets.
"On a Lehmer problem concerning Euler's totient function." Proc. Japan Acad. Ser. A Math. Sci. 79 (8) 136 - 138, Oct. 2003. https://doi.org/10.3792/pjaa.79.136