021.clj

; Problem 21: Amicable numbers
; Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
; If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.

; For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.

; Evaluate the sum of all the amicable numbers under 10000.

(def d (memoize
  (fn [n]
    (loop [i 2 sum 1]
      (let [n-sqrt (Math/sqrt n)]
        (cond (> i n-sqrt)
                sum
              (= i n-sqrt)
                (+ sum i)
              (zero? (rem n i))
                (recur (inc i) (+ sum i (/ n i)))
              :else
                (recur (inc i) sum)))))))

(->>
 (range 10000)
 (filter #(= % (d (d %))))
 (apply +)) ; 40285