Completely multiplicative function
ARITHMETIC FUNCTION THAT IS MULTIPLICATIVE FOR EVERY PAIR OF INTEGERS, NOT NECESSARILY COPRIME
Totally multiplicative; Completely multiplicative; Totally multiplicative function
In number theory, functions of positive integers which respect products are important and are called completely multiplicative functions or totally multiplicative functions. A weaker condition is also important, respecting only products of coprime numbers, and such functions are called multiplicative functions.