Multiplicative and Additive Functions
An arithmetic function a is
- completely additive if a(mn) = a(m) + a(n) for all natural numbers m and n;
- completely multiplicative if a(mn) = a(m)a(n) for all natural numbers m and n;
Two whole numbers m and n are called coprime if their greatest common divisor is 1; i.e., if there is no prime number that divides both of them.
Then an arithmetic function a is
- additive if a(mn) = a(m) + a(n) for all coprime natural numbers m and n;
- multiplicative if a(mn) = a(m)a(n) for all coprime natural numbers m and n.
Read more about this topic: Arithmetic Function
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