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Fungrim entry: 0ba38f

#Gqprimitive=dqφ(d)μ ⁣(qd)\# G_{q}^{\text{primitive}} = \sum_{d \mid q} \varphi(d) \mu\!\left(\frac{q}{d}\right)
Assumptions:qZ1q \in \mathbb{Z}_{\ge 1}
References:
  • http://oeis.org/A007431
TeX:
\# G_{q}^{\text{primitive}} = \sum_{d \mid q} \varphi(d) \mu\!\left(\frac{q}{d}\right)

q \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
Cardinality#S\# S Set cardinality
PrimitiveDirichletCharactersGqprimitiveG_{q}^{\text{primitive}} Primitive Dirichlet characters with given modulus
DivisorSumknf(k)\sum_{k \mid n} f(k) Sum over divisors
Totientφ(n)\varphi(n) Euler totient function
MoebiusMuμ(n)\mu(n) Möbius function
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("0ba38f"),
    Formula(Equal(Cardinality(PrimitiveDirichletCharacters(q)), DivisorSum(Mul(Totient(d), MoebiusMu(Div(q, d))), For(d, q)))),
    Variables(q),
    Assumptions(Element(q, ZZGreaterEqual(1))),
    References("http://oeis.org/A007431"))

Topics using this entry

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

2019-10-05 13:11:19.856591 UTC