用clojure解决euler problem 12

问题描述：

The sequence of triangle numbers is generated by adding the natural numbers. So the 7^thtriangle 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?

解决方案：

(ns euler-problem-12.core
  (:use [clojure.contrib.math]))

(defn prime?
  [num]
 (every? #(or (> (rem num %) 0) (= num %)) (apply list (range 2 (inc (ceil (sqrt num)))))))

(defn next-prime
  [num]
  (loop [x (inc num)]
    (if (prime? x)
      x
      (recur (inc x)))))

(defn prime-factors
  [n]
  (loop
      [curent-n n, p 2, c [ ]]
    (if (prime? curent-n)
      (conj c curent-n)
      (if (= 0 (rem curent-n p))
        (recur (/ curent-n p) p (conj c p))
        (recur curent-n (next-prime p) c)))))

(defn factors-count
  [vprime-factors]
  (loop
      [last-factor nil, factors vprime-factors, counts [1], c-count 2]
    (if (empty? factors)
      (apply * counts)
      (if (= last-factor (first factors))
        (recur last-factor  (rest factors) counts (inc c-count))
        (recur (first factors) (rest factors) (conj counts c-count) 2)))))

(defn first-triangle-number-500-factors
  []
  (loop
      [n 2, t-n 1]
    (if (> (factors-count (prime-factors (+ t-n n))) 500)
      (+ t-n n)
      (recur (inc n) (+ t-n n)))))

(first-triangle-number-500-factors)

答案：76576500