Digit sum of powers in bases
CJam, 13 bytes
q~,f#\fb::+$p

I think this can be improved, but lets get this started.
The input is in the following order : b a n
Example input:
3 2 4

Output:
[1 2 2 4]

Code expansion:
q~             &quot;Read the input and parse it. Now we have on stack, b a and n&quot;
  ,            &quot;Get an array from 0 to n-1&quot;;
   f#          &quot;Get all the powers of a present in the array, i.e. 0 to n-1&quot;;
     \         &quot;Swap the array of a^i and bring the base on top&quot;;
      fb       &quot;For each number in the array, convert it into its base representation array&quot;;
        ::+    &quot;Calculate the sum of each of the sub arrays in the bigger array&quot;;
           $p  &quot;Sort and print the sum of digits of base representation of n powers of a&quot;;

Try it online here