# euler / clojure / 21.clj

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31``` ```; 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. ; ; Answer: 31626 (defn factors [n] (let [max (inc (int (Math/sqrt n)))] (loop [fs [] i 2] (if (= i max) (set (cons 1 fs)) ; Unique items (if (zero? (mod n i)) (recur (concat fs [i (/ n i)]) (inc i)) (recur fs (inc i))))))) (defn d [n] (apply + (factors n))) (defn amicable? [n] (let [i (d n)] (and (not (= n i)) (= (d i) n)))) (prn (apply + (filter amicable? (range 1 10001)))) ```
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