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The Multiplicative Arithmetic Functions Connected with a Finite Abelian Group
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An arithmetic function f(N) is multiplicative if
f(MN)=f(M)f(N)
whenever the integers M, N are relatively prime. The function F(N) defined by the equation
F(N)=Σf1(δ)f2(N/δ)
summed for all divisors δ of N is called the composite of the two arithmetic functions f1, f2. If f1 and f2 are multiplicative, it is easy to see that their composite F (represented by f1, f2) is also multiplicative.
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