theory, functions of positive integers which respect products are important and are called completely multiplicative functions or totally multiplicative functions...

a and b are coprime. 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...

the space. The identity function on the positive integers is a completely multiplicative function (essentially multiplication by 1), considered in number...

Dirichlet convolution of two multiplicative functions is again multiplicative, and every not constantly zero multiplicative function has a Dirichlet inverse...

f is multiplicative, then so is g. If f is completely multiplicative, then g is multiplicative, but may or may not be completely multiplicative. There...

In number theory, the unit function is a completely multiplicative function on the positive integers defined as: ε ( n ) = { 1 , if  n = 1 0 , if  n ≠...

analogy with totally multiplicative functions. If f is a completely additive function then f(1) = 0. Every completely additive function is additive, but not...

an important arithmetic function that is neither multiplicative nor additive. The von Mangoldt function, denoted by Λ(n), is defined as Λ ( n ) = { log...

Idk is the completely multiplicative function Id k ⁡ ( n ) = n k {\displaystyle \operatorname {Id} _{k}(n)=n^{k}} . The divisor function σ k {\displaystyle...

for any lesser integer, where φ is the Euler totient function. Any completely multiplicative function is defined by its values at primorials, since it is...