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Fungrim entry: 08ff0b

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

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

2021-03-15 19:12:00.328586 UTC