# 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 .