Fungrim entry: 0ba38f

\# G^{\text{Primitive}}_{q} = \sum_{d \mid q} \varphi(d) \mu\!\left(\frac{q}{d}\right)

Assumptions:

q \in \mathbb{Z}_{\ge 1}

References:

http://oeis.org/A007431

TeX:

\# G^{\text{Primitive}}_{q} = \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`	$\# S$	Set cardinality
`PrimitiveDirichletCharacters`	$G^{\text{Primitive}}_{q}$	Primitive Dirichlet characters with given modulus
`DivisorSum`	$\sum_{k \mid n} f(k)$	Sum over divisors
`Totient`	$\varphi(n)$	Euler totient function
`MoebiusMu`	$\mu(n)$	Möbius function
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	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

Dirichlet characters