multiplicative function
nounUK /ˌmʌltɪplɪˈkeɪtɪv ˈfʌŋkʃən/
US /ˌmʌltɪplɪˈkeɪtɪv ˈfʌŋkʃən/
A multiplicative function is a math rule where you can multiply the answers for two numbers that share no factors to get the answer for their product.
The Euler phi function is a multiplicative function because phi of 15 equals phi of 3 times phi of 5.
OTHER MEANINGS
2. A function f on positive integers such that f(mn) = f(m)f(n) whenever m and n are coprime.
The divisor-counting function d(n) is multiplicative since d(6) = d(2)d(3).
3. A function that respects multiplication in the sense of preserving products over coprime arguments.
Many multiplicative functions are studied for their values at prime powers.
4. In algebra, a map that distributes over multiplication in a compatible way.
The norm map on a field extension is multiplicative on nonzero elements.