Unit function

In number theory, the unit function is a completely multiplicative function on the positive integers defined as:

$\varepsilon (n)={\begin{cases}1,&{\mbox{if }}n{\mbox{=1}}\\0,&{\mbox{if }}n{>1}\end{cases}}$

This function is the identity element for for Dirichlet convolution.

It may be described as the "indicator function of 1" within the set of positive integers. It is also written as u(n) (not to be confused with μ(n)).

See also

• Möbius inversion formula