Multiplicative Function

In number theory, a multiplicative function is an arithmetic function f(n) of the positive integer n with the property that f(1) = 1 and whenever a and b are coprime, then

f(ab) = f(a) f(b).

An arithmetic function f(n) is said to be completely multiplicative (or totally multiplicative) if f(1) = 1 and f(ab) = f(a) f(b) holds for all positive integers a and b, even when they are not coprime.

Read more about Multiplicative Function:  Examples, Properties, Convolution

Famous quotes containing the word function:

    “The function of muscle is to pull and not to push, except in the case of the genitals and the tongue.”
    —Leonardo Da Vinci (1425–1519)