Fungrim entry: 0477b3

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

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
Totient$\varphi\!\left(n\right)$ Euler totient function
DivisorSigma$\sigma_{k}\!\left(n\right)$ Sum of divisors function
Pow${a}^{b}$ Power
ConstPi$\pi$ 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(ConstPi, 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

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2019-08-17 11:32:46.829430 UTC