= Constant-one arithmetic function
{title2=$\mathbf 1$}
The <constant-one arithmetic function> has $\mathbf1(n)=1$ for every <positive integer> $n$, including $\mathbf1(1)=\mathbf1(12)=1$. It is a <completely multiplicative function>. Its <Dirichlet convolution> with an <arithmetic function> $f$ is the <divisor sum> $(\mathbf1*f)(n)=\sum_{d\mid n}f(d)$. Thus $\mathbf1*\mathbf1=\tau$, the <divisor function>. Its <pointwise product of arithmetic functions> with $f$ is $f$ itself; its <Dirichlet convolution> with $f$ generally is not. The <Identity for Dirichlet convolution> is instead $\varepsilon$.
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