On Lehmer's problem and related problems

We show that if $N\pm 1=M\phi (N)$ with $N\mathrm{\ne }15,255$ composite, then $M<15.76515\log \log \log N$ and $M<16.03235\log \log \omega (N)$, together with similar results for the unitary totient function, Dedekind function, and the sum of unitary divisors.