Difference between revisions of "Landau's function"

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(Created page with '==Definition== Let <math>n</math> be a nonnegative integer. The '''Landau's function''' of <math>n</math> is defined in the following equivalent ways: * The maximum possible va...')
 
 
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* The maximum possible value for the [[least common multiple]] of the parts in an [[unordered integer partition]] of <math>n</math>.
 
* The maximum possible value for the [[least common multiple]] of the parts in an [[unordered integer partition]] of <math>n</math>.
* The maximum of the [[groupprops:order of an element|order]]s of all elements in the symmetric group of degree <math>n</math>.
+
* The maximum of the [[groupprops:order of an element|order]]s of all elements in the [[groupprops:symmetric group|symmetric group]] of degree <math>n</math>.
  
 
The value at <math>n = 0</math> is defined to be <math>1</math>.
 
The value at <math>n = 0</math> is defined to be <math>1</math>.

Latest revision as of 21:00, 30 April 2009

Definition

Let be a nonnegative integer. The Landau's function of is defined in the following equivalent ways:

The value at is defined to be .

Behavior

The ID of the sequence in the Online Encyclopedia of Integer Sequences is A000793

=Initial values

The values of Landau's function for is .

Relation with other functions