Question

Write in C++ Programming (Spring 2020)

Question 5 [15pts]

Write a function to find the first 45 Amicable pairs of numbers (series A259180

on the On-line Encyclopedia of Integer Sequences). A pair of numbers

x

and

y

is called amicable if the

sum of the proper divisors of either one is equal to the other. For example, 220 and 284 is a pair of

amicable numbers. The divisors or 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110. The sum of all those

numbers is equal to 284. The divisors of 284 are 1, 2, 4, 71, 142, which add up to 220. A proper divisor

is one that divides the number without a remainder.

Hint:

use auxiliary functions to break down the

complexity of the task

Answer 1

amicable.cpp

#include<iostream>
#include<math.h>
using namespace std;

//Function to find factorsum
long factorSum(long n)
{
   //sum is intialized to 1 because 1 is factor of every numebrs
   long sum=1;
   //Iterate from 2 to square root of n
   for(int i=2;i<=sqrt(n);i++)
   {
       //If i is a factor of n
       if(n%i==0)
       {
           //49/7 = 7 then add 7 only once
           if(n/i==i)
           {
               sum+=i;
           }
           //Add 2 factors
           else
           {
               sum+=(n/i + i);
           }
       }
   }
   //return sum
   return sum;
}

int main()
{
   long count=0,num=2;
   //Iterate until 45 Amicable pair were found
   while(count<45)
   {
       //find factorsum of num and store in variable sum1
       long sum1 = factorSum(num);
       //find factorsum of sum1 and store in variable sum2
       long sum2 = factorSum(sum1);
       //num!=sum1 becasue factorSum(28)=28 but 28 is not Amicable pair
       //If num is eqaul to sum2 then num, sum1 are Amicable pair
       if(num!=sum1 && num==sum2)
       {
           cout<<num<<" "<<sum1<<endl;
           //next num starts at sum1
           num=sum1;
           //increment the Amicable paris counts
           count++;
       }
       num++;
   }
   return 0;
}

output screenshot: