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=1\\0,&{\mbox{if }}n\neq 1\end{cases}}

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)).

See also

References

↑ Estrada, Ricardo (1995), "Dirichlet convolution inverses and solution of integral equations", Journal of Integral Equations and Applications, 7 (2): 159–166, doi:10.1216/jiea/1181075867, MR 1355233 .

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