Unit function

The unit function is a completely multiplicative function on the positive integers defined as:

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

It is sometimes called multiplication unit for Dirichlet convolution and the Characteristic function of 1. It is also written as u(n), not to be confused with $\mu$(n).

See also

• Möbius inversion formula