Landau's function
From Number
Definition
Let be a nonnegative integer. The Landau's function of
is defined in the following equivalent ways:
- The maximum possible value for the least common multiple of the parts in an unordered integer partition of
.
- The maximum of the orders of all elements in the symmetric group of degree
.
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
- lcm of all numbers so far is the exponent of the symmetric group of degree
.
- factorial is the order (i.e., cardinality) of the symmetric group of degree
.