# Fungrim entry: 32e430

Symbol: LandauG $g\!\left(n\right)$ Landau's function
Landau's function $g\!\left(n\right)$ gives the largest order of an element of the symmetric group ${S}_{n}$.
It can be defined arithmetically as the maximum least common multiple of the partitions of $n$, as in 7932c3.
The following table lists conditions such that LandauG(n) is defined in Fungrim.
Domain Codomain
$n \in \mathbb{Z}_{\ge 0}$ $g\!\left(n\right) \in \mathbb{Z}_{\ge 1}$
Table data: $\left(P, Q\right)$ such that $\left(P\right) \implies \left(Q\right)$
References:
• https://oeis.org/A000793
Definitions:
Fungrim symbol Notation Short description
LandauG$g\!\left(n\right)$ Landau's function
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("32e430"),
SymbolDefinition(LandauG, LandauG(n), "Landau's function"),
Description("Landau's function", LandauG(n), "gives the largest order of an element of the symmetric group", Subscript(S, n), "."),
Description("It can be defined arithmetically as the maximum least common multiple of the partitions of", n, ", as in", EntryReference("7932c3"), "."),
Description("The following table lists conditions such that", SourceForm(LandauG(n)), "is defined in Fungrim."),
Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(Element(n, ZZGreaterEqual(0)), Element(LandauG(n), ZZGreaterEqual(1))))),
References("https://oeis.org/A000793"))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-21 11:44:15.926409 UTC