Are ～つ and ～り the only two counters that can occur with the native Japanese numbers (ひと～, ふた～, etc)?


Please go easy on me if this seems too basic and obvious, I'm a beginner.

I always had the impression that there were counters that went with the native
Japanese numbers and counters that went with the Sino Japanese numbers.

But now I'm wondering if I'm wrong and that only the Sino Japanese numbers are
used with all counters except for some exceptions:

  * ～つ always uses native Japanese numbers:  
ひとつ、ふたつ、みっつ

  * For counting people, only "one" and "two" use native Japanese with ～り and all other numbers use Sino Japanese with ～にん:  
ひとり、ふたり、さんにん

For some reason I find it hard to search for this and what I do find seems to
be poorly worded and convoluted such that I can't extract this little fact
from the discussions easily at all.




Counters for days also use Japanese numerals, from 2 to 10: ふつか, みっか, よっか... .
20th also uses a native counter: はつか.

Some day numbers use mixed counters (14, 24): じゅうよっか, にじゅうよっか.

