I have a really hard time wrapping my head around how this could work.
When one page has 50 types and another 50 as well, they can get 50c max.
But when one page has 90 types and another 10, they can get 10c max.
So ideally I think we should strive for a situation where the max c value would result in a same score.
I did some tests with both formulas and your second formula comes closer to desired numbers.
Edit: Nablator I just now see your edit. Even though the colors are close, your second attempt should still be better. But it's not yet optimal.
When one page has 50 types and another 50 as well, they can get 50c max.
But when one page has 90 types and another 10, they can get 10c max.
So ideally I think we should strive for a situation where the max c value would result in a same score.
I did some tests with both formulas and your second formula comes closer to desired numbers.
Edit: Nablator I just now see your edit. Even though the colors are close, your second attempt should still be better. But it's not yet optimal.