Recall that the digital root of a number, in base 10, is found by adding together the digits of that number, and repeating that process until a number arrives at less than 10. Thus the digital root of 467 is 8.
We shall call a Digital Root Sum (DRS) the sum of the digital roots of the individual factors of our number. The chart below demonstrates all of the DRS values for 24.
| Factorisation | Digital Root Sum |
|---------------|------------------|
| 2x2x2x3 | 9 |
| 2x3x4 | 9 |
| 2x2x6 | 10 |
| 4x6 | 10 |
| 3x8 | 11 |
| 2x12 | 5 |
| 24 | 6 |
The maximum Digital Root Sum of 24 is 11. The function $mdrs(n)$ gives the maximum Digital Root Sum of $n$. So $mdrs(24) = 11$.
Find $\sum{mdrs(n)}$ for $1 < n < 1,000,000$.