  Nicolas criterion for the Riemann Hypothesis is based on an inequality that
Euler totient function must satisfy at primorial numbers. A natural approach to
derive this inequality would be to prove that a specific sequence related to
that bound is strictly decreasing. We show that, unfortunately, this latter
fact would contradict Cram\'er conjecture on gaps between consecutive primes.
An analogous situation holds when replacing Euler totient by Dedekind $\Psi$
function.
