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A Greek mu of a number, valued minus one, zero or one.
Also known as: Möbius function, Mobius mu, Mu function
The Möbius function is 0 if a number has a repeated prime factor, and otherwise ±1 according to whether it has an even or odd number of prime factors. It exists to be inverted: Möbius inversion recovers a function from its divisor sums, which is the standard tool of multiplicative number theory.
Denotes the function valued 0 on numbers with a squared prime factor and ±1 elsewhere by the parity of the prime count.
Contexts: Mathematics
Is the inverse of the constant-one function under Dirichlet convolution, which is what makes Möbius inversion work.
Contexts: Mathematics
A Greek lowercase mu — a rounded form with a descending tail on the left — followed by a bracketed numeral.