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 <algorithm>
       
#include <cmath>
       
 
       
// find greatest common divisor

       
template <typename T>
       
T gcd(T a, T b)
       
{
       
  while (a != 0)
       
  {
       
    T c = a;
       
    a = b % a;
       
    b = c;
       
  }
       
  return b;
       
}
       
 
       
int main()
       
{
       
  // pre-computation step 1: find all triangle combinations up to 1500000
       
  const unsigned int MaxLength = 5 * 1000 * 1000;
       
  // [length] => [number of valid combinations]
       
  std::vector<unsigned int> combinations(MaxLength, 0);
       
 
       
  for (unsigned int m = 2; m < sqrt(MaxLength); m++)
       
    for (unsigned int n = 1; n < m; n++)
       
    {
       
      // only valid m and n
       
      if ((m + n) % 2 != 1)
       
        continue;
       
      if (gcd(m, n) != 1)
       
        continue;
       
 
       
      // compute basic triplet
       
      auto a = m*m - n*n;
       
      auto b = 2*m*n;
       
      auto c = m*m + n*n;
       
      auto sum = a + b + c;
       
 
       
      // and all of its multiples
       
      unsigned int k = 1;
       
      while (k*sum <= MaxLength)
       
      {
       
        combinations[k*sum]++;
       
        k++;
       
      }
       
    }
       
 
       
  // pre-computation step 2: extract those with exactly one combination
       
  std::vector<unsigned int> once;
       
  for (size_t i = 0; i < combinations.size(); i++)
       
    if (combinations[i] == 1)
       
      once.push_back(i);
       
 
       
  // running the test-cases is a simple look-up
       
  unsigned int tests = 1;
       
  std::cin >> tests;
       
  while (tests--)
       
  {
       
    unsigned int limit = 1500000;
       
    std::cin >> limit;
       
 
       
    // find first triangle perimeter exceeding 1500000 with exactly one combination
       
    auto pos = std::upper_bound(once.begin(), once.end(), limit);
       
    // count how many one-combo-triangles are smaller
       
    auto result = std::distance(once.begin(), pos);
       
    // and print that number
       
    std::cout << result << std::endl;
       
  }
       
}

This solution contains 8 empty lines, 11 comments and 4 preprocessor commands.