euler5.clj

(defmacro divides?
  "Return true if y divides x. Expands to (= 0 (mod x y))"
  [x y]
  `(zero? (mod ~x ~y)))

(defn prime?
  "Check to see if a number is prime. Naive"
  [n]
  (let [r (inc (Math/floor (Math/sqrt n)))]
    (nil? (some #(divides? n %) (range 2 r)))))

(defn prime-divisors
  "A lazy-seq of all of the prime divisors of n between 2 and sqrt(n)"
  [n]
  (let [r (inc (Math/floor (Math/sqrt n)))]
    (filter prime? (filter #(divides? n %) (range 2 r)))))

(defn prime-factors
  "Generate the prime factorization of n as a seq"
  [n]
  ((fn [x accum]
    (if (prime? x)
      (cons x accum)
      (let [d (first (prime-divisors x))]
        (recur (/ x d) (cons d accum)))))
   n []))

(defn counts
  "Given a collection, returns a map from items in the collection to the number
  of times they occur"
  [xs]
  (reduce #(assoc %1 %2 (inc (get %1 %2 0))) {} xs))

(defn get-answer []
  (let [factor-counts (map #(counts (prime-factors %)) (range 1 (inc n)))]
    (reduce-kv #(apply * %1 (repeat %3 %2)) 1 (apply merge-with max factor-counts)))))

merge-with is pretty cool. good to know that exists.