LiouvilleLambda

LiouvilleLambda[n]
gives the Liouville function .

Details and OptionsDetails and Options

  • Integer mathematical function, suitable for both symbolic and numerical manipulation.
  • For a number n=u p1k1 pmkm with u a unit and pi primes, LiouvilleLambda[n] returns (-1)k1++km.
  • LiouvilleLambda[n,GaussianIntegers->True] is defined using factorization over Gaussian integers.
  • LiouvilleLambda is a completely multiplicative function.

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Liouville's function gives where is the number of prime factors counting multiplicity:

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Plot the sequence:

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Introduced in 2008
(7.0)
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