Arithmetic function
= Arithmetic function
{title2=$f:\mathbb Z_{>0}\to\mathbb C$}
{wiki}
An <arithmetic function> is a <function> whose <domain of a function> is the <positive integers>, usually taking values in the <complex numbers>. Thus $f(1),f(2),\ldots$ are its values; $f(0)$ is outside this <domain of a function>. Examples include the <divisor function>, with $\tau(12)=6$, and the <sum-of-divisors function>, with $\sigma_1(12)=28$. Studying an <arithmetic function> packages a question about each <positive integer> into one object whose values can be combined using <Dirichlet convolution>. https://darijgrinberg.gitlab.io/floor.pdf[Darij Grinberg, MIT 18.781 lecture notes, Section 2.1: arithmetic functions]{ref}