DLMF:27.3.E7 (Q8008)

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DLMF:27.3.E7
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    Statements

    Defining formula
    σ α ⁡ ( m ) ⁢ σ α ⁡ ( n ) = ∑ d | ( m , n ) d α ⁢ σ α ⁡ ( m ⁢ n d 2 ) , divisor-sigma 𝛼 𝑚 divisor-sigma 𝛼 𝑛 subscript divides 𝑑 𝑚 𝑛 superscript 𝑑 𝛼 divisor-sigma 𝛼 𝑚 𝑛 superscript 𝑑 2 {\displaystyle{\displaystyle\sigma_{\alpha}\left(m\right)\sigma_{\alpha}\left(% n\right)=\sum_{d\mathbin{|}\left(m,n\right)}d^{\alpha}\sigma_{\alpha}\left(% \frac{mn}{d^{2}}\right),}}
    0 references
    DLMF id
    DLMF:27.3.E7
    0 references
    Symbols used
    sum of powers of divisors of $$n$$
    Defining formula
    σ α ⁡ ( n ) divisor-sigma 𝛼 𝑛 {\displaystyle{\displaystyle\sigma_{\NVar{\alpha}}\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E10.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.m6aadec
    0 references
    Q12241
    Defining formula
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C27.S1.XMD1.m1dec
    0 references
    Q12239
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C27.S1.XMD3.m1adec
    0 references
    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1fdec
    0 references
     
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