= Pointwise product of arithmetic functions
{title2=$(f\cdot g)(n)=f(n)g(n)$}
The <pointwise product of arithmetic functions> multiplies two <arithmetic functions> at the same input: $(f\cdot g)(n)=f(n)g(n)$. Thus $(\mathbf1\cdot\mathbf1)(12)=1$ and $(\operatorname{id}\cdot\mathbf1)(12)=12$, using the <constant-one arithmetic function> and the <identity arithmetic function>. These differ from the corresponding <Dirichlet convolution> values $6$ and $28$, because <Dirichlet convolution> sums over every positive <integer divisor>.
Back to article page
