The Ainu counting system is simple but the etymology is intriguing. There are lots of pages in Japanese with tables of data which you can consult for the details, but the summary is: there are roots for the numbers one through five (/sine/, /tu/, /re/, /ine/, /asikne/), ten (/wan/), and twenty (/hot/). Everything else is (etymologically) a combination of those roots.

As Kirsten REFSING puts it in The Ainu Language,

6 to 9 are derived by deducting 4, 3, 2, and 1 respectively from 10. I-wan is this "four (i < ine) - ten (wan)"; and arwan should be "three - ten", where ar < re, according to Chiri (1936). Tupesan [8] and sinepsan [9] are usually interpreted as tu/sine + p + e + san, i.e. "two/one - thing - thereby - ten", where san < wan. However, a more likely interpretation of these last two numerals is suggested by Patrie (1981). He traces their origin back to an alternate morpheme for "ten", namely upis, which is found in Kurile Ainu as documented in the 18th century by Krascheninnikov and Steller independently (see Murayama: 1971). Thus tupesan is from tu-upis and sinepesan from sine-upis. The final -an remains to be accounted for, but it may perhaps be connected with the existential verb an.

Meanwhile, /asikne/ (five) is probably related to a word meaning "hand" or "finger", and "hot" apparently has something to do with a word meaning "set" (as in, one person's full set of digits, I suppose.)

Interestingly, "six" (the first number without its own morpheme) is the official Ainu number for "lots and lots", kind of like "eight" in Japanese.