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pe_021.cpp
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pe_021.cpp
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#include <iostream>
#include "timer.h"
/*/
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.
/*/
int sum_prop_div(const int &n) {
int sum = 1;
for(int i=2; i*i<=n; i++)
if(n%i==0) sum += i + (i*i==n? 0 : n/i);
return sum;
}
int main() {
const int CAP = 10000;
int sum = 0;
//attempt1
{
Timer t;
//starting at 2 because 1 is the only number with only itself as its factors
for(int i = 2; i<CAP; i++)
if(i == sum_prop_div(sum_prop_div(i)) && sum_prop_div(i) != i)
sum += i;
}
std::cout<<sum<<std::endl;
return 0;
}