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Fungrim entry: 3d5019

log ⁣(g(n))nlog(n)\log\!\left(g(n)\right) \ge \sqrt{n \log(n)}
Assumptions:nZ906n \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
Loglog(z)\log(z) Natural logarithm
LandauGg(n)g(n) Landau's function
Sqrtz\sqrt{z} Principal square root
ZZGreaterEqualZn\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"))

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2019-10-05 13:11:19.856591 UTC