In 256 bytes or fewer write a function, \$f\$, from the positive integers to the positive integers that is:
Monotonic: larger inputs always map to larger outputs. (\$a < b \implies f(a) < f(b)\$)
Non-linear: does not have asymptotic order notation \$O(n)\$. (\$\displaystyle\forall c: \exists n:c\cdot n < f(n)\$)
Your answers will be scored by the asymptotic Big-O order notation of the function they implement (run time is irrelevant) with smaller being better. In the case of a tie the size of the code is the tie breaker.
You may implement a function or a complete program. Since we are concerned with asymptotic complexity your program should accept input of arbitrary size.