Factoring

Implement the function

val factor : int -> (int * int) list

so that factor n computes the prime factorization of n and returns it as a list of pairs of a prime factor and its corresponding exponent. That is, if n can be written as \(p_1^{e_1} \cdot p_2^{e_2} \cdots p_k^{e_k}\), then factor n should be [(p1, e1); (p2, e2); ...; (pk, ek)], with the primes appearing in increasing order. The behavior of the function is undefined if the input is not positive.

let _ = assert (factor 1 = [])
let _ = assert (factor 19 = [(19,1)])
let _ = assert (factor 16 = [(2,4)])
let _ = assert (factor 360 = [(2,3);(3,2);(5,1)])