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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

- Multiplicative arithmetic functions
- Completely multiplicative arithmetic functions
- Additive arithmetic functions
- Completely additive arithmetic functions

## Notes

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