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- Liouville_function abstract "The Liouville function, denoted by λ(n) and named after Joseph Liouville, is an important function in number theory.If n is a positive integer, then λ(n) is defined as:where Ω(n) is the number of prime factors of n, counted with multiplicity (sequence A008836 in OEIS).λ is completely multiplicative since Ω(n) is completely additive. The number one has no prime factors, so Ω(1) = 0 and therefore λ(1) = 1. The Liouville function satisfies the identity:The Liouville function's Dirichlet inverse is the absolute value of the Möbius function.".
- Liouville_function thumbnail Liouville.svg?width=300.
- Liouville_function wikiPageID "104463".
- Liouville_function wikiPageRevisionID "570809153".
- Liouville_function author "A.F. Lavrik".
- Liouville_function hasPhotoCollection Liouville_function.
- Liouville_function id "L/l059620".
- Liouville_function title "Liouville Function".
- Liouville_function title "Liouville function".
- Liouville_function urlname "LiouvilleFunction".
- Liouville_function subject Category:Multiplicative_functions.
- Liouville_function type Abstraction100002137.
- Liouville_function type Function113783816.
- Liouville_function type MathematicalRelation113783581.
- Liouville_function type MultiplicativeFunctions.
- Liouville_function type Relation100031921.
- Liouville_function comment "The Liouville function, denoted by λ(n) and named after Joseph Liouville, is an important function in number theory.If n is a positive integer, then λ(n) is defined as:where Ω(n) is the number of prime factors of n, counted with multiplicity (sequence A008836 in OEIS).λ is completely multiplicative since Ω(n) is completely additive. The number one has no prime factors, so Ω(1) = 0 and therefore λ(1) = 1.".
- Liouville_function label "Fonction de Liouville".
- Liouville_function label "Función de Liouville".
- Liouville_function label "Funzione di Liouville".
- Liouville_function label "Liouville function".
- Liouville_function label "Liouville-Funktion".
- Liouville_function label "Liouville-functie".
- Liouville_function label "دالة ليوفيل".
- Liouville_function label "劉維爾函數".
- Liouville_function sameAs Liouville-Funktion.
- Liouville_function sameAs Función_de_Liouville.
- Liouville_function sameAs Fonction_de_Liouville.
- Liouville_function sameAs Funzione_di_Liouville.
- Liouville_function sameAs Liouville-functie.
- Liouville_function sameAs m.0q5cz.
- Liouville_function sameAs Q385019.
- Liouville_function sameAs Q385019.
- Liouville_function sameAs Liouville_function.
- Liouville_function wasDerivedFrom Liouville_function?oldid=570809153.
- Liouville_function depiction Liouville.svg.
- Liouville_function isPrimaryTopicOf Liouville_function.
