Problem #21

This one took me a bit...first I didnt notice that (6,6) (and others like that) are not pairs, the pairs have to be different numbers. Second I was only going up to 1000, not 10000, and third I was counting the number of pairs, not the sum of the numbers...but I eventually got it down. Heres the C++ code to solve this one:

#include <iostream>

using namespace std;

int sumDivisors (int);

int main()
{
    int total = 0;
    bool allNums[10000];

    for (unsigned int i = 0; i < 10000; i++)
        allNums[i] = false;
 
    for (unsigned int i = 0; i < 10000; i++)
        if (i == sumDivisors (sumDivisors (i)) && i != sumDivisors (i))
            allNums[i] = allNums[sumDivisors (i)] = true;

    for (unsigned int i = 0; i < 10000; i++)
        if (allNums[i] == true)
            total += i;

    cout << total << endl;

    system("pause");
    return 0;
}

int sumDivisors (int num)
{
    int total = 0;

    for (unsigned int i = 1; i < static_cast<unsigned int> (num / 2 + 1); i++)
        if (num % i == 0)
            total += i;

    return total;
}