Fungrim entry: 4b5b44

\lim_{n \to \infty} \frac{\varphi(n)}{{n}^{1 - \delta}} = \infty

Assumptions:

\delta \in \left(0, \infty\right)

TeX:

\lim_{n \to \infty} \frac{\varphi(n)}{{n}^{1 - \delta}} = \infty

\delta \in \left(0, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`SequenceLimit`	$\lim_{n \to a} f(n)$	Limiting value of sequence
`Totient`	$\varphi(n)$	Euler totient function
`Pow`	${a}^{b}$	Power
`Infinity`	$\infty$	Positive infinity
`OpenInterval`	$\left(a, b\right)$	Open interval

Source code for this entry:

Entry(ID("4b5b44"),
    Formula(Equal(SequenceLimit(Div(Totient(n), Pow(n, Sub(1, delta))), For(n, Infinity)), Infinity)),
    Variables(delta),
    Assumptions(Element(delta, OpenInterval(0, Infinity))))

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