Fungrim entry: 86fcf1

\# \left\{ n : n \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \varphi(n) < \frac{n}{{e}^{\gamma} \log\!\left(\log(n)\right)} \right\}

TeX:

\# \left\{ n : n \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \varphi(n) < \frac{n}{{e}^{\gamma} \log\!\left(\log(n)\right)} \right\}

\# \mathbb{Z}

Definitions:

Fungrim symbol	Notation	Short description
`Cardinality`	$\# S$	Set cardinality
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`Totient`	$\varphi(n)$	Euler totient function
`Exp`	${e}^{z}$	Exponential function
`ConstGamma`	$\gamma$	The constant gamma (0.577...)
`Log`	$\log(z)$	Natural logarithm
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("86fcf1"),
    Formula(Equal(Cardinality(Set(n, ForElement(n, ZZGreaterEqual(1)), Less(Totient(n), Div(n, Mul(Exp(ConstGamma), Log(Log(n)))))))), Cardinality(ZZ)))

Topics using this entry

Totient function

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