Average digit sum – 6

Let $s(n)$ be the digit sum of $n$ .

$d_a(n)$ is defined to be the average digit sum of all non-negative integers less than or equal to $n$ that are divisible by $a$ .

$d_a(n)= \displaystyle \frac 1{\left\lfloor \frac na \right\rfloor +1} \sum_{k=0}^{\left\lfloor \frac na \right\rfloor} s(ak)$

Find the maximum number of integers $a$ in a set $A = \{a_1,a_2,a_3,\ldots,a_m\}$ such that $d_{a_i}\left(10^6-1\right) = d_{a_j}\left(10^6-1\right)$ for any $1 \leq i,j \leq m$ and $a_1=1$ .

Other parts

• Average digit sum – 5