Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
If d(a) = b and d(b) = a, where a b, then a and b are an amicable pair and each of a and b are called amicable numbers.
For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.
Evaluate the sum of all the amicable numbers under 10000.
2
3 using namespace std;
4
5 int SumOfDivisors(int num)
6 {
7 int sum = 1;
8 for(int i=2; i<sqrt((float)num); i++)
9 {
10 if(num % i == 0)
11 {
12 sum += i + num /i;
13 }
14 }
15 return sum;
16 }
17
18 int main()
19 {
20 long sum = 0;
21 for(int i=1; i<10000; i++)
22 {
23 int value = SumOfDivisors(i);
24 if(value != i && SumOfDivisors(value) == i)
25 {
26 sum += i;
27 }
28 }
29
30 cout << sum << endl;
31 cin.get();
32 }