  We give a new formula for the Chebotarev densities of Frobenius elements in
Galois groups. This formula is given in terms of smallest prime factors
$p_{\mathrm{min}}(n)$ of integers $n\geq2$. More precisely, let $C$ be a
conjugacy class of the Galois group of some finite Galois extension $K$ of
$\mathbb{Q}$. Then we prove that
$$-\lim_{X\rightarrow\infty}\sum_{\substack{2\leq n\leq
X\\[1pt]\left[\frac{K/\mathbb{Q}}{p_{\mathrm{min}}(n)}\right]=C}}\frac{\mu(n)}{n}=\frac{\#C}{\#G}.$$
This theorem is a generalization of a result of Alladi from 1977 that asserts
that largest prime divisors $p_{\mathrm{max}}(n)$ are equidistributed in
arithmetic progressions modulo an integer $k$, which occurs when $K$ is a
cyclotomic field $\mathbb{Q}(\zeta_k)$.
