012.clj

; Problem 12: Highly divisible triangular number
; The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:

; 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

; Let us list the factors of the first seven triangle numbers:

;  1: 1
;  3: 1,3
;  6: 1,2,3,6
; 10: 1,2,5,10
; 15: 1,3,5,15
; 21: 1,3,7,21
; 28: 1,2,4,7,14,28
; We can see that 28 is the first triangle number to have over five divisors.

; What is the value of the first triangle number to have over five hundred divisors?

(defn triangle-numbers []
  (drop 1 (map first (iterate (fn [[t n]] [(+ t n) (inc n)]) [0 1]))))

(defn numfactors [n]
  (let [nsqrt (Math/sqrt n)]
    (loop [nf 0 i 1]
      (cond (> i nsqrt) nf
            (== i nsqrt) (inc nf)
            :default (recur (if (zero? (mod n i)) (+ 2 nf) nf)
                            (inc i))))))

(first (filter #(<= 500 (numfactors %)) (triangle-numbers))) ; 76576500