Fungrim entry: 0477b3

\varphi(n) \sigma_{1}\!\left(n\right) > \frac{6}{{\pi}^{2}} {n}^{2}

Assumptions:

n \in \mathbb{Z}_{\ge 1}

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) > \frac{6}{{\pi}^{2}} {n}^{2}

n \in \mathbb{Z}_{\ge 1}

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
`Pi`	$\pi$	The constant pi (3.14...)
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("0477b3"),
    Formula(Greater(Mul(Totient(n), DivisorSigma(1, n)), Mul(Div(6, Pow(Pi, 2)), Pow(n, 2)))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))),
    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