MoebiusMu

The Möbius function: 0 if n has a squared prime factor, else (-1)^(number of prime factors).

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MoebiusMu(n)the Möbius function .

SageMathmoebius(n)SymPymobius(n)

Domain: Number theory

Details

if has a squared prime factor; otherwise for distinct prime factors.
by convention, the empty product.
Underlies Möbius inversion: for every .
is squarefree exactly when . See IsSquareFree.
is only defined on positive integers; compute-engine leaves unevaluated.

Examples

See also: FactorInteger, IsSquareFree