Cyclic-group Lehmer constant conjecture

For an integer $n\geqslant2$, let $\rho(n)$ denote the smallest prime number that does not divide $n$. For the cyclic group $\mathbb{Z}_{\!/n}$, let $\lambda(\mathbb{Z}_{\!/n})$ denote its Lehmer constant. Cyclic-group Lehmer constant conjecture.

$$\lambda(\mathbb{Z}_{\!/n})=\frac1n\log\rho(n)$$

for all $n\geqslant2$. The theorem preceding this conjecture gives the same expression as an upper bound, and the equality is known from computations for $n=2,3,4$; the conjecture asserts that this upper bound is always attained.