DLMF:27.10.E5 (Q8062)

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DLMF:27.10.E5
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    Statements

    Defining formula
    c k ⁡ ( n ) = ∑ d | ( n , k ) d ⁢ μ ⁡ ( k d ) . Ramanujan-sum 𝑘 𝑛 subscript divides 𝑑 𝑛 𝑘 𝑑 Moebius-mu 𝑘 𝑑 {\displaystyle{\displaystyle c_{k}\left(n\right)=\sum_{d\mathbin{|}\left(n,k% \right)}d\mu\left(\frac{k}{d}\right).}}
    0 references
    DLMF id
    DLMF:27.10.E5
    0 references
    Symbols used
    Möbius function
    Defining formula
    μ ⁡ ( n ) Moebius-mu 𝑛 {\displaystyle{\displaystyle\mu\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E12.m2adec
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    Ramanujan’s sum
    Defining formula
    c k ⁡ ( n ) Ramanujan-sum 𝑘 𝑛 {\displaystyle{\displaystyle c_{\NVar{k}}\left(\NVar{n}\right)}}
    xml-id
    C27.S10.E4.m2aadec
    0 references
    Q12093
    Defining formula
    ( m , n ) 𝑚 𝑛 {\displaystyle{\displaystyle\left(\NVar{m},\NVar{n}\right)}}
    xml-id
    C27.S1.p2.t1.r3.m6adec
    0 references
    Q12241
    Defining formula
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C27.S1.XMD1.m1dec
    0 references
    Q12238
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C27.S1.XMD2.m1ddec
    0 references
     
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