My code

… was written in C++ 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 <vector>
       
#include <cmath>
       
 
       
int main()
       
{
       
  // five dummy entries
       
  std::vector<long long> cache(5, 0);
       
 
       
#define ORIGINAL
       
#ifndef ORIGINAL
       
  unsigned int tests = 1;
       
  std::cin >> tests;
       
  while (tests--)
       
#endif
       
  {
       
    unsigned int limit = 10000;
       
    std::cin >> limit;
       
 
       
    auto result = cache.back();
       
    for (unsigned int n = cache.size(); n <= limit; n++)
       
    {
       
      unsigned int k = round(n / 2.718281828);
       
 
       
      // terminating only if n/k has only prime factors 2 and 5
       
      while (k % 5 == 0)
       
        k /= 5;
       
      while (k % 2 == 0)
       
        k /= 2;
       
 
       
      if (n % k == 0)
       
        result -= n;
       
      else
       
        result += n;
       
 
       
      // cache intermediate results, too (needed for Hackerrank only)
       
      cache.push_back(result);
       
    }
       
 
       
    // display result
       
    std::cout << cache[limit] << std::endl;
       
  }
       
 
       
  return 0;
       
}

This solution contains 8 empty lines, 4 comments and 6 preprocessor commands.