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 <vector>
       
#include <algorithm>
       
 
       
//#define ORIGINAL

       
 
       
// find digit root of a number

       
unsigned int digitRoot(unsigned int x)
       
{
       
  // taken from https://en.wikipedia.org/wiki/Digital_root
       
  //return ((x - 1) % 9) + 1;
       
 
       
  // and my original code:
       
  unsigned int result = 0;
       
  while (x > 0)
       
  {
       
    result += x % 10;
       
    x      /= 10;
       
  }
       
 
       
  // repeat again ?
       
  if (result >= 10)
       
    result = digitRoot(result);
       
 
       
  return result;
       
}
       
 
       
int main()
       
{
       
  unsigned int limit = 1000000;
       
 
       
#ifndef ORIGINAL
       
  // read all test cases
       
  limit = 1;
       
  unsigned int tests = 1;
       
  std::cin >> tests;
       
  std::vector<unsigned int> input(tests);
       
  for (auto& x : input)
       
  {
       
    std::cin >> x;
       
    if (limit < x)
       
      limit = x;
       
  }
       
#endif
       
 
       
  // step 1: precompute sum(mdrs) for every x
       
 
       
  std::vector<unsigned char> mdrs(limit + 1, 0);
       
 
       
  // digit root without any factorization
       
  for (unsigned int i = 2; i <= limit; i++)
       
    mdrs[i] = digitRoot(i);
       
 
       
  // for each number a ...
       
  for (unsigned int a = 2; a <= limit; a++)
       
    // ... adjust all its multiples a*b
       
    for (unsigned int b = 2; a * b <= limit && b <= a; b++)
       
      // improved ?
       
      if (mdrs[a * b] < mdrs[a] + mdrs[b])
       
        mdrs[a * b] = mdrs[a] + mdrs[b];
       
 
       
  // step 2: display result(s)
       
 
       
#ifdef ORIGINAL
       
  // sum of mdrs(2..limit-1)
       
  unsigned int sum = 0;
       
  for (unsigned int i = 2; i < limit; i++)
       
    sum += mdrs[i];
       
 
       
  std::cout << sum << std::endl;
       
#else
       
  // sum of mdrs(2..i) for every 2 <= i <= limit
       
  // note: unlike the original problem, it is including limit
       
  std::vector<unsigned int> sums(mdrs.size(), 0);
       
  for (unsigned int i = 2; i < sums.size(); i++)
       
    sums[i] = sums[i-1] + mdrs[i];
       
 
       
  // display results
       
  for (auto x : input)
       
    std::cout << sums[x] << std::endl;
       
#endif
       
 
       
  return 0;
       
}

This solution contains 16 empty lines, 17 comments and 8 preprocessor commands.