If f(mn) = f(m)*f(n) even when m and n are not relatively prime, then f is called totally multiplicative. Some multiplicative functions include: the divisor function, the sigma function and Euler's totient function. One totally multiplicative function is Liouville's lambda function.

# Multiplicative (idea)

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An adjective used to describe an arithmetic function for which the product of the function on two relatively prime integers is the same as the function of the product of the two numbers.
That is, if gcd(m,n) = 1, then f(x) is multiplicitave iff f(mn) = f(m)f(n).