How to resolve the algorithm Amicable pairs step by step in the Clojure programming language

Published on 12 May 2024 09:40 PM
#Clojure

How to resolve the algorithm Amicable pairs step by step in the Clojure programming language

Table of Contents

Problem Statement

Two integers

N

{\displaystyle N}

and

M

{\displaystyle M}

are said to be amicable pairs if

N ≠ M

{\displaystyle N\neq M}

and the sum of the proper divisors of

N

{\displaystyle N}

(

s u m

(

p r o p D i v s

( N ) )

{\displaystyle \mathrm {sum} (\mathrm {propDivs} (N))}

)

= M

{\displaystyle =M}

as well as

s u m

(

p r o p D i v s

( M ) )

N

{\displaystyle \mathrm {sum} (\mathrm {propDivs} (M))=N}

.

1184 and 1210 are an amicable pair, with proper divisors:

Calculate and show here the Amicable pairs below 20,000; (there are eight).

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Amicable pairs step by step in the Clojure programming language

Source code in the clojure programming language

(ns example
  (:gen-class))

(defn factors [n]
  " Find the proper factors of a number "
  (into (sorted-set)
        (mapcat (fn [x] (if (= x 1) [x] [x (/ n x)]))
                (filter #(zero? (rem n %)) (range 1 (inc (Math/sqrt n)))) )))


(def find-pairs (into #{}
               (for [n (range  2 20000)
                  :let [f (factors n)     ; Factors of n
                        M (apply + f)     ; Sum of factors
                        g (factors M)     ; Factors of sum
                        N (apply + g)]    ; Sum of Factors of sum
                  :when (= n N)           ; (sum(proDivs(N)) = M and sum(propDivs(M)) = N
                  :when (not= M N)]       ; N not-equal M
                 (sorted-set n M))))      ; Found pair

;; Output Results
(doseq [q find-pairs]
  (println q))

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