Fungrim entry: acb28a

\varphi(n) \sigma_{1}\!\left(n\right) < {n}^{2}

Assumptions:

n \in \mathbb{Z}_{\ge 2}

References:

G. H. Hardy and E. M. Wright (1979), An Introduction to the Theory of Numbers (Fifth ed.), Oxford University Press. Theorem 327.

TeX:

\varphi(n) \sigma_{1}\!\left(n\right) < {n}^{2}

n \in \mathbb{Z}_{\ge 2}

Definitions:

Fungrim symbol	Notation	Short description
`Totient`	$\varphi(n)$	Euler totient function
`DivisorSigma`	$\sigma_{k}\!\left(n\right)$	Sum of divisors function
`Pow`	${a}^{b}$	Power
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("acb28a"),
    Formula(Less(Mul(Totient(n), DivisorSigma(1, n)), Pow(n, 2))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(2))),
    References("G. H. Hardy and E. M. Wright (1979), An Introduction to the Theory of Numbers (Fifth ed.), Oxford University Press. Theorem 327."))

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