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.

The code contains #ifdefs to switch between the original problem and the Hackerrank version.
Enable #ifdef ORIGINAL to produce the result for the original problem (default setting for most problems).

       
#include <iostream>
       
#include <iomanip>
       
#include <vector>
       
#include <map>
       
 
       
int main()
       
{
       
  unsigned long long limit = 4000000;
       
  std::cin >> limit;
       
 
       
#define ORIGINAL
       
#ifdef ORIGINAL
       
  // 12 primes are enough for the original problem, I added a few more for the Hackerrank version
       
  const unsigned int NumPrimes = 12;
       
  // a short list of primes
       
  unsigned int primes[] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 };
       
#else
       
  const unsigned int NumPrimes = 18;
       
  // a short list of primes
       
  unsigned int primes[] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61 };
       
#endif
       
 
       
  // use 1 as a "seed" value (all its primes' exponents are zero)
       
  typedef std::vector<unsigned char> Exponents;
       
  std::map<long double, Exponents> todo = { { 1, Exponents(NumPrimes, 0) } };
       
 
       
  while (true)
       
  {
       
    // pick the smallest value and its exponents
       
    auto current   = todo.begin();
       
    auto value     = current->first;
       
    auto exponents = current->second;
       
 
       
    // remove from todo list
       
    todo.erase(current);
       
 
       
    // find number of factorizations
       
    unsigned long long uniqueFactors = 1;
       
    for (auto x : exponents)
       
      uniqueFactors *= 2 * x + 1;
       
    // a*b = b*a => divide number of factorizations by 2
       
    uniqueFactors++;
       
    uniqueFactors /= 2;
       
 
       
    // stop ?
       
    if (uniqueFactors >= limit)
       
    {
       
      std::cout << std::fixed << std::setprecision(0) << value << std::endl;
       
      break;
       
    }
       
 
       
    // increment each primes' exponent by 1 and append new value to todo list
       
    for (size_t i = 0; i < exponents.size(); i++)
       
    {
       
#ifdef ORIGINAL
       
      // speed optimization: exponents of larger primes can be at most 1
       
      if (exponents[i] == 1 && i > 3) // 3 was found by trial-n-error
       
        break;
       
#endif
       
 
       
      exponents[i]++;
       
      value *= primes[i];
       
 
       
      todo[value] = exponents;
       
      // note: std::map prunes duplicates automatically
       
    }
       
  }
       
 
       
  return 0;
       
}

This solution contains 11 empty lines, 12 comments and 10 preprocessor commands.