It's math notation invented for analytic number theory that got popularized in CS by Donald Knuth. By definition, constant (nonzero) arguments denote the same

It's math notation invented for analytic number theory that got popularized in CS by Donald Knuth. By definition, constant (nonzero) arguments denote the same class, so using constants different from 1 isn't really useful. However, the O stands for 'order' or 'order of', and it sometimes gets (ab)used to denote orders of magnitude (eg powers of 10) of finite values instead of limiting behaviour of functions.