Landau's function

Definition

Let $n$ be a nonnegative integer. The Landau's function of $n$ 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 $n$.
• The maximum of the orders of all elements in the symmetric group of degree $n$.

The value at $n=0$ is defined to be $1$.

Behavior

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

=Initial values

The values of Landau's function for $n=0,1,2,3,4,5,6,7$ is $1,1,2,3,4,6,6,12$.

Relation with other functions

• lcm of all numbers so far is the exponent of the symmetric group of degree $n$.
• factorial is the order (i.e., cardinality) of the symmetric group of degree $n$.