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# 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

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2019-10-05 13:11:19.856591 UTC