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DLMF:27.5.E4 - MaRDI portal

DLMF:27.5.E4 (Q8721)

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DLMF:27.5.E4
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    Statements

    DLMF defining formula
    n = ∑ d | n ϕ ⁡ ( d ) ⟺ ϕ ⁡ ( n ) = ∑ d | n d ⁢ μ ⁡ ( n d ) , ⟺ 𝑛 subscript divides 𝑑 𝑛 Euler-totient-phi 𝑑 Euler-totient-phi 𝑛 subscript divides 𝑑 𝑛 𝑑 Moebius-mu 𝑛 𝑑 {\displaystyle{\displaystyle n=\sum_{d\mathbin{|}n}\phi\left(d\right)% \Longleftrightarrow\phi\left(n\right)=\sum_{d\mathbin{|}n}d\mu\left(\frac{n}{d% }\right),}}
    0 references
    Symbols used
    Euler’s totient
    DLMF defining formula
    ϕ ⁡ ( n ) Euler-totient-phi 𝑛 {\displaystyle{\displaystyle\phi\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E7.m2adec
    0 references
    Möbius function
    DLMF defining formula
    μ ⁡ ( n ) Moebius-mu 𝑛 {\displaystyle{\displaystyle\mu\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E12.m2abdec
    0 references
    positive integer
    DLMF defining formula
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C27.S1.XMD1.m1cdec
    0 references
    positive integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1cdec
    0 references

    Identifiers

     
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