Landau's function

Definition

Let $\text{[math]}$ be a nonnegative integer. The Landau's function of $\text{[math]}$ 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 $\text{[math]}$ .
The maximum of the orders of all elements in the symmetric group of degree $\text{[math]}$ .

The value at $\text{[math]}$ is defined to be $\text{[math]}$ .

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

The values of Landau's function for $\text{[math]}$ is $\text{[math]}$ .

lcm of all numbers so far is the exponent of the symmetric group of degree $\text{[math]}$ .
factorial is the order (i.e., cardinality) of the symmetric group of degree $\text{[math]}$ .