MöbiusMu

The Möbius function.

Syntax

• MöbiusMu(n)

  • n is a positive integer

Description

If n is a positive integer, then

              ⎧ +1   if n is square-free and has an even number of prime factors
MöbiusMu(n) = ⎨ −1   if n is square-free and has an odd number of prime factors
              ⎩  0   if n is not square-free.

Examples

MöbiusMu(219557911565161)

−1

SequenceVector(25) @ MöbiusMu

(1, −1, −1, 0, −1, 1, −1, 0, 0, 1, −1, 0, −1, 1, 1, 0, −1, 0, −1, 0, 1, 1, −1, 0, 0)

∑(SequenceVector(100000) @ MöbiusMu)

−48

∑(SequenceVector(100000) @ MöbiusMu @ abs)

60794

n ≔ 12345; ∑(divisors(n) @ MöbiusMu)

0

See also

• Mertens