multiplicative functions

A multiplicative function is a kind of mathematical function that relates to whole numbers and has a special property: when you multiply two numbers that don't share any common factors (called coprime numbers), the function’s value at their product is the same as multiplying the function’s values at each number separately. For example, if the function is called f, and two coprime numbers are a and b, then f(a × b) = f(a) × f(b). These functions are important in number theory because they help analyze how numbers are built from prime factors and how various number properties behave under multiplication.