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Completely multiplicative functions

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In number theory, completely multiplicative arithmetic functions are arithmetic functions such that[1]

This is to say that it doesn't matter whether and are coprime or not (i.e. share or don't share prime factors), as opposed to multiplicative arithmetic functions which require coprimality.

See also


  1. Outside of number theory, the term multiplicative function usually means "completely" multiplicative function, and the domain is not restricted to the positive integers.