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Fungrim entry: 08ff0b

φ ⁣(n)=ndn,d<nφ ⁣(d)\varphi\!\left(n\right) = n - \sum_{d \mid n,\, d < n} \varphi\!\left(d\right)
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
TeX:
\varphi\!\left(n\right) = n - \sum_{d \mid n,\, d < n} \varphi\!\left(d\right)

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Totientφ ⁣(n)\varphi\!\left(n\right) Euler totient function
DivisorSumknf ⁣(k)\sum_{k \mid n} f\!\left(k\right) Sum over divisors
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("08ff0b"),
    Formula(Equal(Totient(n), Sub(n, DivisorSum(Totient(d), d, n, Less(d, 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.

2019-08-17 11:32:46.829430 UTC