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Fungrim entry: b9c50f

φ(n)=n∏p∣n(1−1p)\varphi(n) = n \prod_{p \mid n} \left(1 - \frac{1}{p}\right)
Assumptions:n∈Z≥1n \in \mathbb{Z}_{\ge 1}
TeX:
\varphi(n) = n \prod_{p \mid n} \left(1 - \frac{1}{p}\right)

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
Totientφ(n)\varphi(n) Euler totient function
PrimeProduct∏pf(p)\prod_{p} f(p) Product over primes
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("b9c50f"),
    Formula(Equal(Totient(n), Mul(n, PrimeProduct(Parentheses(Sub(1, Div(1, p))), For(p), Divides(p, 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.

2021-03-15 19:12:00.328586 UTC