Number of monic irreducible polynomials over a finite field ($N_q(n)$)

Let $N_q(n)$ be the number of monic irreducible polynomials of polynomial degree $n$ over ${\mathbb{F}}_q$. Factoring $X^{q^n}-X$ into all such polynomials whose degrees divide $n$ givesThe Möbius inversion formula therefore gives