I have a function that looks like $$f_n(i) = \max\left(\left\lfloor \frac{i-n}{2} \right \rfloor + 1, 0\right)$$
and I would like to write it as a nice arithmetic function. To give an idea, another example where I can find a suitable answer is $$g_n(i) = \max\left(i-n+1, 0\right)$$
where I get $g_n(i+n) = i+1 = \tau(p^{i})$.
But in the case of $f$ it would end with something like $\tau(p^{\lfloor i/2\rfloor})$, and... it does not seem very multiplicative, is it?