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:
“Uses are always much broader than functions, and usually far less contentious. The word function carries overtones of purpose and propriety, of concern with why something was developed rather than with how it has actually been found useful. The function of automobiles is to transport people and objects, but they are used for a variety of other purposes—as homes, offices, bedrooms, henhouses, jetties, breakwaters, even offensive weapons.”
—Frank Smith (b. 1928)