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Fungrim entry: acb28a

φ ⁣(n)σ1 ⁣(n)<n2\varphi\!\left(n\right) \sigma_{1}\!\left(n\right) < {n}^{2}
Assumptions:nZ2n \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\!\left(n\right) \sigma_{1}\!\left(n\right) < {n}^{2}

n \in \mathbb{Z}_{\ge 2}
Definitions:
Fungrim symbol Notation Short description
Totientφ ⁣(n)\varphi\!\left(n\right) Euler totient function
DivisorSigmaσk ⁣(n)\sigma_{k}\!\left(n\right) Sum of divisors function
Powab{a}^{b} Power
ZZGreaterEqualZn\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."))

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2019-08-19 14:38:23.809000 UTC