This system is the same as that used to apportion the US House, which is called the method of equal proportions.
Step 1: Give each State a seat (Region a delegate).
Step 2: Determine for each State its priority value.
The priority value is equal to the population of the State divided by the square root of n*(n+1) where n is the number of seats it current has. At the start this will be dividing all populations by the square root of 2 (2=1*2) to get the priority values, then by the square root of 6 (6=2*3), square root of 12 (12=3*4) etc. as States add seats.
Step 3: Give the State with the largest priority value a seat and recalculate its priority value based on the fact that it has an extra seat.
Step 4: Until you have the number of seats you want, repeat Step 3.
(Or alternatively, you could decide a priori that the cutoff will be at a certain priority value, if you don't want a fixed size for the group.
Thank you for that explaination.