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Fungrim entry: c0e088

φ ⁣(2n)={2φ(n),n evenφ(n),n odd\varphi\!\left(2 n\right) = \begin{cases} 2 \varphi(n), & n \text{ even}\\\varphi(n), & n \text{ odd}\\ \end{cases}
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
TeX:
\varphi\!\left(2 n\right) = \begin{cases} 2 \varphi(n), & n \text{ even}\\\varphi(n), & n \text{ odd}\\ \end{cases}

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Totientφ(n)\varphi(n) Euler totient function
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("c0e088"),
    Formula(Equal(Totient(Mul(2, n)), Cases(Tuple(Mul(2, Totient(n)), Even(n)), Tuple(Totient(n), Odd(n))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-12-11 23:01:54.699850 UTC