My code

… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, too. Or just jump to my GitHub repository.

       
#include <iostream>
       
#include <vector>
       
#include <cmath>
       
 
       
// greatest common divisor

       
unsigned int gcd(unsigned int a, unsigned int b)
       
{
       
  while (a != 0)
       
  {
       
    unsigned int c = a;
       
    a = b % a;
       
    b = c;
       
  }
       
  return b;
       
}
       
 
       
int main()
       
{
       
  unsigned int limit  = 120000;
       
  std::cin >> limit;
       
 
       
  // sieve-like computation of rad
       
  std::vector<unsigned int> rad(limit, 1);
       
  for (unsigned int i = 2; i < limit; i++)
       
  {
       
    // if rad(i) > 1 then "a" is not prime
       
    if (rad[i] > 1)
       
      continue;
       
 
       
    // process all multiples of a
       
    for (unsigned int j = 1; i*j < limit; j++)
       
      rad[i*j] *= i;
       
  }
       
 
       
  // walk through all potential a and b
       
  unsigned long long sum = 0;
       
  for (unsigned int a = 1; a < limit/2; a++)
       
  {
       
    unsigned int incrementB = 1;
       
    // make sure that if a is even then b is always odd
       
    if (a % 2 == 0)
       
      incrementB = 2;
       
 
       
    for (unsigned int b = a + 1; a + b < limit; b += incrementB)
       
    {
       
      auto c = a + b;
       
 
       
      // this check is much faster than the gcd()-computation and eliminates most candidates
       
      auto prodRad = rad[a] * rad[b] * (unsigned long long)rad[c];
       
      if (prodRad >= c)
       
        continue;
       
 
       
      // no shared prime factors
       
      if (gcd(rad[a], rad[b]) != 1)
       
        continue;
       
 
       
      // yes, found another abc-hit
       
      sum += c;
       
    }
       
  }
       
 
       
  // display result
       
  std::cout << sum << std::endl;
       
 
       
  return 0;
       
}

This solution contains 11 empty lines, 10 comments and 3 preprocessor commands.