Eccoci.

A composite number can be factored many different ways. For instance, not including multiplication by one, $24$ can be factored in $7$ distinct ways:

\begin{align} 24 &= 2 \times 2 \times 2 \times 3\\ 24 &= 2 \times 3 \times 4\\ 24 &= 2 \times 2 \times 6\\ 24 &= 4 \times 6\\ 24 &= 3 \times 8\\ 24 &= 2 \times 12\\ 24 &= 24 \end{align}

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 is arrived at that is 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
$2 \times 2 \times 2 \times 3$	$9$
$2 \times 3 \times 4$	$9$
$2 \times 2 \times 6$	$10$
$4 \times 6$	$10$
$3 \times 8$	$11$
$2 \times 12$	$5$
$24$	$6$

The maximum Digital Root Sum of $24$ is $11$.
The function $\operatorname{mdrs}(n)$ gives the maximum Digital Root Sum of $n$. So $\operatorname{mdrs}(24)=11$.
Find $\sum \operatorname{mdrs}(n)$ for $1 \lt n \lt 1\,000\,000$.