DLMF:27.10.E5 (Q8062): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Ramanujan’s sum / rank
 
Normal rank
Property / Symbols used: Ramanujan’s sum / qualifier
 
Defining formula:

c k ( n ) Ramanujan-sum 𝑘 𝑛 {\displaystyle{\displaystyle c_{\NVar{k}}\left(\NVar{n}\right)}}

\Ramanujansum{\NVar{k}}@{\NVar{n}}
Property / Symbols used: Ramanujan’s sum / qualifier
 
xml-id: C27.S10.E4.m2aadec

Revision as of 14:23, 2 January 2020

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DLMF:27.10.E5
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    Statements

    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).}}
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    DLMF:27.10.E5
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    μ ( n ) Moebius-mu 𝑛 {\displaystyle{\displaystyle\mu\left(\NVar{n}\right)}}
    C27.S2.E12.m2adec
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    c k ( n ) Ramanujan-sum 𝑘 𝑛 {\displaystyle{\displaystyle c_{\NVar{k}}\left(\NVar{n}\right)}}
    C27.S10.E4.m2aadec
    0 references