How to resolve the algorithm Abundant, deficient and perfect number classifications step by step in the AppleScript programming language

Published on 12 May 2024 09:40 PM
#Applescript

How to resolve the algorithm Abundant, deficient and perfect number classifications step by step in the AppleScript programming language

Table of Contents

Problem Statement

These define three classifications of positive integers based on their   proper divisors. Let   P(n)   be the sum of the proper divisors of   n   where the proper divisors are all positive divisors of   n   other than   n   itself.

6   has proper divisors of   1,   2,   and   3. 1 + 2 + 3 = 6,   so   6   is classed as a perfect number.

Calculate how many of the integers   1   to   20,000   (inclusive) are in each of the three classes. Show the results here.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Abundant, deficient and perfect number classifications step by step in the AppleScript programming language

Source code in the applescript programming language

on aliquotSum(n)
    if (n < 2) then return 0
    set sum to 1
    set sqrt to n ^ 0.5
    set limit to sqrt div 1
    if (limit = sqrt) then
        set sum to sum + limit
        set limit to limit - 1
    end if
    repeat with i from 2 to limit
        if (n mod i is 0) then set sum to sum + i + n div i
    end repeat
    
    return sum
end aliquotSum

on task()
    set {deficient, perfect, abundant} to {0, 0, 0}
    repeat with n from 1 to 20000
        set s to aliquotSum(n)
        if (s < n) then
            set deficient to deficient + 1
        else if (s > n) then
            set abundant to abundant + 1
        else
            set perfect to perfect + 1
        end if
    end repeat
    
    return {deficient:deficient, perfect:perfect, abundant:abundant}
end task

task()


{deficient:15043, perfect:4, abundant:4953}

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