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Fungrim entry: 433a5c

φ ⁣(n)>neγlog ⁣(log ⁣(n))+2.50637log ⁣(log ⁣(n))\varphi\!\left(n\right) > \frac{n}{{e}^{\gamma} \log\!\left(\log\!\left(n\right)\right) + \frac{2.50637}{\log\!\left(\log\!\left(n\right)\right)}}
Assumptions:nZ3n \in \mathbb{Z}_{\ge 3}
TeX:
\varphi\!\left(n\right) > \frac{n}{{e}^{\gamma} \log\!\left(\log\!\left(n\right)\right) + \frac{2.50637}{\log\!\left(\log\!\left(n\right)\right)}}

n \in \mathbb{Z}_{\ge 3}
Definitions:
Fungrim symbol Notation Short description
Totientφ ⁣(n)\varphi\!\left(n\right) Euler totient function
Expez{e}^{z} Exponential function
ConstGammaγ\gamma The constant gamma (0.577...)
Loglog ⁣(z)\log\!\left(z\right) Natural logarithm
ZZGreaterEqualZn\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

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2019-08-19 14:38:23.809000 UTC