Arithmetic derivative
= Arithmetic derivative
{title2=$n'$}
The arithmetic derivative on <positive integers> is defined by $p\prime=1$ for every <prime> $p$ and the <product rule> $(ab)\prime=a\prime b+ab\prime$. For $n=\prod_i p_i^{e_i}$, these rules give $n\prime=n\sum_i e_i/p_i$. In particular, $(p^e)\prime=e p^{e-1}$.