Series $1$, $1$, $\frac12$, $\frac12$, $\frac13$, $\frac13$, etc.

Question

Is there any way to define an analytical function in a region that's contained by 0 and 1 that will correspond with the following series:

$1$, $1$, $\frac12$, $\frac12$, $\frac13$, $\frac13$, $\dots$, $\frac{1}{n}$, $\frac{1}{n}$

(such that $f(1) = 1, f(2) = 1, f(3) = \frac12, f(4) = \frac12, \dots$)?

I've tried using some combinations of exponents and $\sin$ but couldn't find any.

Thanks in advance!