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Fungrim entry: efd378

φ(n)=∑d∣nμ(d)nd\varphi(n) = \sum_{d \mid n} \mu(d) \frac{n}{d}
Assumptions:n∈Z≥0n \in \mathbb{Z}_{\ge 0}
TeX:
\varphi(n) = \sum_{d \mid n} \mu(d) \frac{n}{d}

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Totientφ(n)\varphi(n) Euler totient function
DivisorSum∑k∣nf(k)\sum_{k \mid n} f(k) Sum over divisors
MoebiusMuμ(n)\mu(n) Möbius function
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("efd378"),
    Formula(Equal(Totient(n), DivisorSum(Mul(MoebiusMu(d), Div(n, d)), For(d, 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.

2021-03-15 19:12:00.328586 UTC