 Pointwise product of arithmetic functions

The pointwise product of arithmetic functions multiplies two arithmetic functions at the same input: $(f\cdot g)(n)=f(n)g(n)$. Thus $(1\cdot 1)(12)=1$ and $(\mathrm{id}\cdot 1)(12)=12$, 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.