  The manuscript reviews Dirichlet Series of important multiplicative
arithmetic functions. The aim is to represent these as products and ratios of
Riemann zeta-functions, or, if that concise format is not found, to provide the
leading factors of the infinite product over zeta-functions. If rooted at the
Dirichlet series for powers, for sums-of-divisors and for Euler's totient, the
inheritance of multiplicativity through Dirichlet convolution or ordinary
multiplication of pairs of arithmetic functions generates most of the results.

Number Theory