Digital root sums of factorisations

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

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

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 mdrs(n) gives the maximum Digital Root Sum of n. So mdrs($24$)=$11$.

Find ∑ mdrs(n) for $1$ < n < $1$,$000$,$000$.