DLMF:27.3.E6 (Q8007): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: sum of powers of divisors of $$n$$ / rank
 
Normal rank
Property / Symbols used: sum of powers of divisors of $$n$$ / qualifier
 
Defining formula:

σ α ⁡ ( n ) divisor-sigma 𝛼 𝑛 {\displaystyle{\displaystyle\sigma_{\NVar{\alpha}}\left(\NVar{n}\right)}}

\sumdivisors{\NVar{\alpha}}@{\NVar{n}}
Property / Symbols used: sum of powers of divisors of $$n$$ / qualifier
 
xml-id: C27.S2.E10.m2adec

Revision as of 14:15, 2 January 2020

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DLMF:27.3.E6
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    Statements

    Defining formula
    σ α ⁡ ( n ) = ∏ r = 1 ν ⁡ ( n ) p r α ⁢ ( 1 + a r ) - 1 p r α - 1 , divisor-sigma 𝛼 𝑛 superscript subscript product 𝑟 1 number-of-primes-dividing-nu 𝑛 subscript superscript 𝑝 𝛼 1 subscript 𝑎 𝑟 𝑟 1 subscript superscript 𝑝 𝛼 𝑟 1 {\displaystyle{\displaystyle\sigma_{\alpha}\left(n\right)=\prod_{r=1}^{\nu% \left(n\right)}\frac{p^{\alpha(1+a_{r})}_{r}-1}{p^{\alpha}_{r}-1},}}
    0 references
    DLMF id
    DLMF:27.3.E6
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    constraint
    α ≠ 0 𝛼 0 {\displaystyle{\displaystyle\alpha\neq 0}}
    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.m2adec
    0 references
     
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