[math-fun] T-Free English Ordinals

Because written-out American English ordinals (first, second, third, fourth, ...) mostly end in "th", I thought it might be fun to count those ordinals that are letter-t-free. There are only 7 less than 10^6 but (I think) already 392 less than 10^9. How many are there less than 10^63 (one vigintillion)? In that range there are ten -illion names without the letter "t".