unit function

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

:

It is called the unit function because it is the identity element for Dirichlet convolution.{{citation

| last = Estrada | first = Ricardo

| doi = 10.1216/jiea/1181075867

| issue = 2

| journal = Journal of Integral Equations and Applications

| mr = 1355233

| pages = 159–166

| title = Dirichlet convolution inverses and solution of integral equations

| volume = 7

| year = 1995| doi-access = free

}}.

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 $\backslash mu(n)$, which generally denotes the Möbius function).