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Fungrim entry: 86fcf1

#{n:nZ1andφ ⁣(n)<neγlog ⁣(log ⁣(n))}=#Z\# \left\{ n : n \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \varphi\!\left(n\right) < \frac{n}{{e}^{\gamma} \log\!\left(\log\!\left(n\right)\right)} \right\} = \# \mathbb{Z}
TeX:
\# \left\{ n : n \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \varphi\!\left(n\right) < \frac{n}{{e}^{\gamma} \log\!\left(\log\!\left(n\right)\right)} \right\} = \# \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
Cardinality#S\# S Set cardinality
SetBuilder{f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
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
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("86fcf1"),
    Formula(Equal(Cardinality(SetBuilder(n, n, And(Element(n, ZZGreaterEqual(1)), Less(Totient(n), Div(n, Mul(Exp(ConstGamma), Log(Log(n)))))))), Cardinality(ZZ))))

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

2019-08-19 14:38:23.809000 UTC