Problem 42453. Divisible by n, prime vs. composite divisors

In general, there are two types of divisibility checks; the first involves composite divisors and the second prime divisors, including powers of prime numbers (technically composite divisors, though they often function similar to prime numbers for the sake of divisibility). We'll get into the specifics of the two divisibility check types in subsequent problems. For now, we'll segregate numbers into three groups, based on type (n_type) while also returning the number's highest-power factorization (hpf). Write a function to return these two variables for a given number; see the following examples for reference:

n = 11  |  n_type = 1 (prime)        |  hpf = [11]
n = 31  |  n_type = 1 (prime)        |  hpf = [31]
n = 9   |  n_type = 2 (prime power)  |  hpf = [9] (3^2)
n = 32  |  n_type = 2 (prime power)  |  hpf = [32] (2^5)
n = 49  |  n_type = 2 (prime power)  |  hpf = [49] (7^2)
n = 21  |  n_type = 3 (composite)    |  hpf = [3,7]
n = 39  |  n_type = 3 (composite)    |  hpf = [3,13]
n = 42  |  n_type = 3 (composite)    |  hpf = [2,3,7]
n = 63  |  n_type = 3 (composite)    |  hpf = [9,7] ([3^2,7])
n = 90  |  n_type = 3 (composite)    |  hpf = [2,9,5] ([2,3^2,5])

Previous problem: divisible by 16. Next problem: Divisible by n, prime divisors (including powers).