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Fungrim entry: bb4ce0

φ ⁣(n)=2nk=1n{k,gcd ⁣(n,k)=10,otherwise\varphi\!\left(n\right) = \frac{2}{n} \sum_{k=1}^{n} \begin{cases} k, & \gcd\!\left(n, k\right) = 1\\0, & \text{otherwise}\\ \end{cases}
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
TeX:
\varphi\!\left(n\right) = \frac{2}{n} \sum_{k=1}^{n} \begin{cases} k, & \gcd\!\left(n, k\right) = 1\\0, & \text{otherwise}\\ \end{cases}

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Totientφ ⁣(n)\varphi\!\left(n\right) Euler totient function
Sumnf ⁣(n)\sum_{n} f\!\left(n\right) Sum
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("bb4ce0"),
    Formula(Equal(Totient(n), Mul(Div(2, n), Sum(Cases(Tuple(k, Equal(GCD(n, k), 1)), Tuple(0, Otherwise)), Tuple(k, 1, n))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

Topics using this entry

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

2019-08-19 14:38:23.809000 UTC