# Fungrim entry: 3d5019

$\log\!\left(g(n)\right) \ge \sqrt{n \log(n)}$
Assumptions:$n \in \mathbb{Z}_{\ge 906}$
References:
• Jean-Pierre Massias, Jean-Louis Nicolas and Guy Robin (1989), Effective bounds for the maximal order of an element in the symmetric group, Mathematics of Computation, 53, 118, pp. 665-665, https://doi.org/10.1090/s0025-5718-1989-0979940-4
TeX:
\log\!\left(g(n)\right) \ge \sqrt{n \log(n)}

n \in \mathbb{Z}_{\ge 906}
Definitions:
Fungrim symbol Notation Short description
Log$\log(z)$ Natural logarithm
LandauG$g(n)$ Landau's function
Sqrt$\sqrt{z}$ Principal square root
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("3d5019"),
Formula(GreaterEqual(Log(LandauG(n)), Sqrt(Mul(n, Log(n))))),
Variables(n),
Assumptions(Element(n, ZZGreaterEqual(906))),
References("Jean-Pierre Massias, Jean-Louis Nicolas and Guy Robin (1989), Effective bounds for the maximal order of an element in the symmetric group, Mathematics of Computation, 53, 118, pp. 665-665, https://doi.org/10.1090/s0025-5718-1989-0979940-4"))

## Topics using this entry

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2021-03-15 19:12:00.328586 UTC