= Identity arithmetic function
{title2=$\operatorname{id}$}
The <identity arithmetic function> is $\operatorname{id}(n)=n$ on the <positive integers>, for example $\operatorname{id}(1)=1$ and $\operatorname{id}(12)=12$. It is a <completely multiplicative function> and gives the <sum-of-divisors function> through $\operatorname{id}*\mathbf1=\sigma_1$ under <Dirichlet convolution>. It is distinct from the <Identity for Dirichlet convolution> $\varepsilon$. The identity $\operatorname{id}=\mathbf1*\varphi$, where $\varphi$ is <Euler's totient function>, is equivalent to $\sum_{d\mid n}\varphi(d)=n$.
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