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Fungrim entry: 433a5c

φ(n)>neγlog⁡ ⁣(log⁡(n))+2.50637log⁡ ⁣(log⁡(n))\varphi(n) > \frac{n}{{e}^{\gamma} \log\!\left(\log(n)\right) + \frac{2.50637}{\log\!\left(\log(n)\right)}}
Assumptions:n∈Z≥3n \in \mathbb{Z}_{\ge 3}
TeX:
\varphi(n) > \frac{n}{{e}^{\gamma} \log\!\left(\log(n)\right) + \frac{2.50637}{\log\!\left(\log(n)\right)}}

n \in \mathbb{Z}_{\ge 3}
Definitions:
Fungrim symbol Notation Short description
Totientφ(n)\varphi(n) Euler totient function
Expez{e}^{z} Exponential function
ConstGammaγ\gamma The constant gamma (0.577...)
Loglog⁡(z)\log(z) Natural logarithm
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("433a5c"),
    Formula(Greater(Totient(n), Div(n, Add(Mul(Exp(ConstGamma), Log(Log(n))), Div(Decimal("2.50637"), Log(Log(n))))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(3))))

Topics using this entry

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

2021-03-15 19:12:00.328586 UTC