# Fungrim entry: bb4ce0

$\varphi(n) = \frac{2}{n} \sum_{k=1}^{n} \begin{cases} k, & \gcd\!\left(n, k\right) = 1\\0, & \text{otherwise}\\ \end{cases}$
Assumptions:$n \in \mathbb{Z}_{\ge 1}$
TeX:
\varphi(n) = \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 1}
Definitions:
Fungrim symbol Notation Short description
Totient$\varphi(n)$ Euler totient function
Sum$\sum_{n} f(n)$ Sum
GCD$\gcd\!\left(a, b\right)$ Greatest common divisor
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ 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)), For(k, 1, n))))),
Variables(n),
Assumptions(Element(n, ZZGreaterEqual(1))))

## Topics using this entry

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

2019-11-19 15:10:20.037976 UTC