By an arithmetical function f, we mean a map f : ℕ → ℂ, where ℕ denotes the set of positive integers and ℂ stands for the set of complex numbers. The ring A https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781351023344/5296d79c-24f0-4b6f-8cb8-ae49e4bf109c/content/eq621.tif"/> of arithmetical functions (under addition and Dirichlet composition) is shown to be a UFD by an isomorphism with ℂ ω , the ring of formal powers series in countably infinite indeterminates. This elegant theorem is due to E. D. Cashwell and C. J. Everett (1959) [ 3 ].