(ns primos)

(defn not-divide? [m n]
  (or
    (= m n)
    (not (zero? (mod m n)))))

(defn criba [n]
  (let [raiz (-> n (Math/sqrt) (Math/ceil) (int))]
    (loop [lista (cons 2 (range 3 (inc n) 2))
           elm   3]
      (if (< elm raiz)
        (let [nueva_lista (filter (fn [n] (not-divide? n elm)) lista)]
          (recur nueva_lista
                 (some #(if (> % elm) % false) nueva_lista)))
        lista))))

(defn divisores [n]
  (let [criba-n (criba (/ n 2))]
    (loop [n-actual n
           divis    []]
      (if (> n-actual 1)
        (let [divisible? (fn [primo] (if (zero? (mod n-actual primo)) primo false))
              divisor    (or (some divisible? criba-n) n-actual)]
          (recur (/ n-actual divisor)
                 (cons divisor divis)))
        divis))))

;(println (divisores (* 2 128473)))