Question

A perfect number is a positive integer that equals the sum of all of its divisors (including the divisor 1 but excluding the number itself). For example 6, 28 and 496 are perfect numbers because 6=1+2+3 28 1 + 2 + 4 + 7 + 14 496 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 Write a program to read a positive integer value, N, and find the smallest perfect number that is strictly greater than N.

Answer 1

#include <iostream>
using namespace std;
// function to check if a number is perfect
bool isperfect(int n){
//initilize variables
int i=1,sum=0;
//loop untill i is less than n
while(i<n){
// if i is a divisor add i to sum
if(n%i==0){
sum=sum+i;
}
i++;
}
// if sum and n are equal it is perfect
if(sum==n)
return true;
else
return false;
}

int main(){
int n,m;
//get input from user
cout << "Enter a number:";
cin >> n;
// copy m to n
m = n;
// loop until perfect number is found by incrementing n
while(!isperfect(++n));
// print output
cout << n << " Is the smallest perfect number greater than " << m;
return 0;
}
/*
sample output
Enter a number: 10
28 Is the smallest perfect number greater than 10
*/

Answer 2

#include <iostream>
using namespace std;
// function to check if a number is perfect
bool isperfect(int n){
//initilize variables
int i=1,sum=0;
//loop untill i is less than n
while(i<n){
// if i is a divisor add i to sum
if(n%i==0){
sum=sum+i;
}
i++;
}
// if sum and n are equal it is perfect
if(sum==n)
return true;
else
return false;
}
int main(){
int n,m;
//get input from user
cout << "Enter a number:";
cin >> n;
// copy m to n
m = n;
// loop until perfect number is found by incrementing n
while(!isperfect(++n));
// print output
cout << n << " Is the smallest perfect number greater than " << m;
return 0;
}