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- Landau's_function abstract "In mathematics, Landau's function g(n), named after Edmund Landau, is defined for every natural number n to be the largest order of an element of the symmetric group Sn. Equivalently, g(n) is the largest least common multiple (lcm) of any partition of n, or the maximum number of times a permutation of n elements can be recursively applied to itself before it returns to its starting sequence.For instance, 5 = 2 + 3 and lcm(2,3) = 6. No other partition of 5 yields a bigger lcm, so g(5) = 6. An element of order 6 in the group S5 can be written in cycle notation as (1 2) (3 4 5).The integer sequence g(0) = 1, g(1) = 1, g(2) = 2, g(3) = 3, g(4) = 4, g(5) = 6, g(6) = 6, g(7) = 12, g(8) = 15, ... (sequence A000793 in OEIS) is named after Edmund Landau, who proved in 1902 that(where ln denotes the natural logarithm).The statement thatfor all sufficiently large n, where Li−1 denotes the inverse of the logarithmic integral function, is equivalent to the Riemann hypothesis.It can be shown that:".
- Landau's_function wikiPageID "138677".
- Landau's_function wikiPageRevisionID "541134336".
- Landau's_function hasPhotoCollection Landau's_function.
- Landau's_function name "Landau's function on the natural numbers".
- Landau's_function sequencenumber "A000793".
- Landau's_function subject Category:Group_theory.
- Landau's_function subject Category:Permutations.
- Landau's_function type Abstraction100002137.
- Landau's_function type Change107296428.
- Landau's_function type Event100029378.
- Landau's_function type Happening107283608.
- Landau's_function type Permutations.
- Landau's_function type PsychologicalFeature100023100.
- Landau's_function type Substitution107443761.
- Landau's_function type Variation107337390.
- Landau's_function type YagoPermanentlyLocatedEntity.
- Landau's_function comment "In mathematics, Landau's function g(n), named after Edmund Landau, is defined for every natural number n to be the largest order of an element of the symmetric group Sn. Equivalently, g(n) is the largest least common multiple (lcm) of any partition of n, or the maximum number of times a permutation of n elements can be recursively applied to itself before it returns to its starting sequence.For instance, 5 = 2 + 3 and lcm(2,3) = 6. No other partition of 5 yields a bigger lcm, so g(5) = 6.".
- Landau's_function label "Fonction de Landau".
- Landau's_function label "Funzione di Landau".
- Landau's_function label "Landau's function".
- Landau's_function label "Landausfunctie".
- Landau's_function label "Функция Ландау".
- Landau's_function label "蘭道函數".
- Landau's_function sameAs Fonction_de_Landau.
- Landau's_function sameAs Funzione_di_Landau.
- Landau's_function sameAs Landausfunctie.
- Landau's_function sameAs m.010zl0.
- Landau's_function sameAs Q967147.
- Landau's_function sameAs Q967147.
- Landau's_function sameAs Landau's_function.
- Landau's_function wasDerivedFrom Landau's_function?oldid=541134336.
- Landau's_function isPrimaryTopicOf Landau's_function.