p12.clj

;; project euler problem 12

(use 
  'clojure.contrib.math 
  'clojure.contrib.lazy-seqs 
  'clojure.contrib.combinatorics)

(def triangles
  (rest (map first (iterate (fn [[a b]] [(+ a b) (inc b)]) [0 1]))))

(defn factor-of? [a b]
  (= 0 (mod a b)))

(defn smallest [xs]
  (first (sort xs)))

(defn exp-range-max [n factors]
  (/ n (smallest factors)))

(defn prime-factors-of [n]
  (filter #(factor-of? n %) (take-while #(< % n) primes)))

(defn raise-nums [nums exps]
  (map (fn [[b e]] (expt b e)) (partition 2 (interleave nums exps))))

(defn exp-combo-works? [n factors powers]
  (= n (apply * (raise-nums factors powers))))

(defn possible-powers [n factors]
  (range 1 (inc (exp-range-max n factors))))

(defn find-exp-combo [n factors]
  (first (drop-while #(not (exp-combo-works? n factors %))
              (selections (possible-powers n factors) (count factors)))))

(defn num-divisors [n]
  (let [combo (find-exp-combo n (prime-factors-of n))]
    (apply * (map inc combo))))

(num-divisors 36) ;should be 9
(take 10 (map num-divisors triangles));brokt