Fungrim home page

Fungrim entry: acb28a

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

n \in \mathbb{Z}_{\ge 2}
Definitions:
Fungrim symbol Notation Short description
Totientφ(n)\varphi(n) 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."))

Topics using this entry

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