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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.^{[1]}

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*), which generally denotes the Möbius function).