Problem Statement

The prime decomposition of a number is defined as a list of prime numbers which when all multiplied together, are equal to that number.

Write a function which returns an array or collection which contains the prime decomposition of a given number

n

{\displaystyle n}

greater than   1. If your language does not have an isPrime-like function available, you may assume that you have a function which determines whether a number is prime (note its name before your code). If you would like to test code from this task, you may use code from trial division or the Sieve of Eratosthenes. Note: The program must not be limited by the word size of your computer or some other artificial limit; it should work for any number regardless of size (ignoring the physical limits of RAM etc).

Let's start with the solution:

(defun factors (n)
  (factors n 2 '()))

(defun factors
  ((1 _ acc)
    acc)
  ((n k acc) (when (== 0 (rem n k)))
    (factors (div n k) k (cons k acc)))
  ((n k acc)
    (factors n (+ k 1) acc)))