Definition
(f * g)(n) = sum_{ab=n} f(a) g(b). Commutative + associative.
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Identity
ε(1) = 1, ε(n) = 0 otherwise. f * ε = f.
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Möbius as inverse of 1
μ * 1 = ε where 1(n) = 1. Enables Möbius inversion.
Multiplicative closure
Product of multiplicative functions is multiplicative. Basis of computing φ, σ, d via prime decomposition.