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>
       
 
       
// user-defined limits

       
unsigned int limit = 1000000000;
       
unsigned int hamming = 100;
       
 
       
// short list of involved primes

       
std::vector<unsigned int> primes;
       
 
       
// return number of hamming numbers where one prime factor is at least primes[indexMinPrime]
       
// and which is a multiple of x

       
unsigned int search(unsigned long long x = 1, unsigned int indexMinPrime = 0)
       
{
       
  unsigned int result = 1;
       
 
       
  // multiply current number by all allowed primes
       
  for (auto i = indexMinPrime; i < primes.size(); i++)
       
  {
       
    auto product = primes[i] * x;
       
 
       
    // too large ?
       
    if (product > limit)
       
      break;
       
 
       
    // multiply by more primes
       
    result += search(product, i);
       
  }
       
 
       
  return result;
       
}
       
 
       
int main()
       
{
       
  std::cin >> hamming >> limit;
       
 
       
  // the usual prime sieve
       
  for (unsigned int i = 2; i <= hamming; i++)
       
  {
       
    bool isPrime = true;
       
    for (auto p : primes)
       
    {
       
      if (p*p > i)
       
        break;
       
      if (i % p == 0)
       
      {
       
        isPrime = false;
       
        break;
       
      }
       
    }
       
 
       
    if (isPrime)
       
      primes.push_back(i);
       
  }
       
 
       
  // count hamming numbers
       
  std::cout << search() << std::endl;
       
}

This solution contains 11 empty lines, 9 comments and 2 preprocessor commands.