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Arithmetic function

In number theory, an arithmetic function (or number-theoretic function) f(n) is a function defined for all positive integers and having values in the complex numbers. In other words: an arithmetic function is nothing but a sequence of complex numbers.

The most important arithmetic functions are the additive and the multiplicative ones.

An important operation on arithmetic functions is the Dirichlet convolution.


The articles on additive and multiplicative functions contain several examples of arithmetic functions. Here are some examples that are neither additive nor multiplicative:

1 = 12+02+02+02 = 02+12+02+02 = 02+02+12+02 = 02+02+02+12,

hence c4(1)=4.