density of low degree factors of X^N-1 in finite fields

Question

Let N be an exponential number of the order O(p^n) for some p and n. How to estimate the density of (or as fraction of N) cardinalities of subsets of polynomials f(X) in GF(p)[X] such that

1.f(X) is irreducible in GF(p). 2. f(X)|(X^N-1) (f(X) divides X^N-1). 3. Degree of f(X)<O(n^k) (polynomial order in n).