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DLMF:27.6.E5 - MaRDI portal

DLMF:27.6.E5 (Q8730)

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DLMF:27.6.E5
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    Statements

    DLMF defining formula
    ∑ d | n | μ ⁡ ( d ) | ϕ ⁡ ( d ) = n ϕ ⁡ ( n ) , subscript divides 𝑑 𝑛 Moebius-mu 𝑑 Euler-totient-phi 𝑑 𝑛 Euler-totient-phi 𝑛 {\displaystyle{\displaystyle\sum_{d\mathbin{|}n}\frac{|\mu\left(d\right)|}{% \phi\left(d\right)}=\frac{n}{\phi\left(n\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.m2acdec
    0 references
    positive integer
    DLMF defining formula
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C27.S1.XMD1.m1ddec
    0 references
    positive integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1ddec
    0 references

    Identifiers

     
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