# Fungrim entry: 86fcf1

$\# \left\{ n : n \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \varphi\!\left(n\right) < \frac{n}{{e}^{\gamma} \log\!\left(\log\!\left(n\right)\right)} \right\} = \# \mathbb{Z}$
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$\# S$ Set cardinality
SetBuilder$\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}$ Set comprehension
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Totient$\varphi\!\left(n\right)$ Euler totient function
Exp${e}^{z}$ Exponential function
ConstGamma$\gamma$ The constant gamma (0.577...)
Log$\log\!\left(z\right)$ Natural logarithm
ZZ$\mathbb{Z}$ 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))))

## Topics using this entry

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