Project Euler 5

Project Euler 5.clj

(use 'clojure.contrib.test-is)
(use 'clojure.contrib.trace)

(with-test
  (defn prime-factorials [n]
    (if (= n 1)
      '()
      (if-let [
        divisor
        (some 
          #(when (zero? (mod n %)) %)
          (range 2 (inc n)))]
        (cons divisor (prime-factorials (/ n divisor))))))
  (are (= (prime-factorials _1) _2)
    1 []
    2 [2]
    3 [3]
    4 [2 2]
    5 [5]
    8 [2 2 2]))

(with-test
  (defn but [seq elem]
    (if-not (some #{elem} seq)
      seq
      (loop [result [] seq seq]
        (if (= (first seq) elem)
          (concat result (rest seq))
          (recur (conj result (first seq)) (rest seq))))))
  (are (= (but _1 _2) _3)
    [1]     1 []
    [1 2]   1 [2]
    [1 2]   0 [1 2]
    []      1 []
    [1 2 3] 3 [1 2]))

(with-test
  (defn difference [seq1 seq2]
    (if (empty? seq2)
      seq1
      (difference (but seq1 (first seq2)) (rest seq2))))
  (are (= (difference _1 _2) _3)
    []    []  []
    []    [1] []
    [1]   [1] []
    [1]   []  [1]
    [1 1] [1] [1]))

(reduce
  *
  (reduce
    (fn [result seq]
      (concat result (difference seq result)))
    (map
      prime-factorials
      (range 1 21))))

(run-tests)