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

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Property / Symbols used
 
Property / Symbols used: Q12234 / rank
 
Normal rank
Property / Symbols used: Q12234 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12234 / qualifier
 
xml-id: C27.S1.XMD4.m1edec
Property / Symbols used
 
Property / Symbols used: Q12235 / rank
 
Normal rank
Property / Symbols used: Q12235 / qualifier
 
Defining formula:

p , p 1 , … 𝑝 subscript 𝑝 1 … {\displaystyle{\displaystyle p,p_{1},\ldots}}

p,p_{1},\ldots
Property / Symbols used: Q12235 / qualifier
 
xml-id: C27.S1.XMD5.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12244 / rank
 
Normal rank
Property / Symbols used: Q12244 / qualifier
 
Defining formula:

a r subscript 𝑎 𝑟 {\displaystyle{\displaystyle a_{r}}}

a_{r}
Property / Symbols used: Q12244 / qualifier
 
xml-id: C27.S2.XMD1.m1bdec

Latest revision as of 14:15, 2 January 2020

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DLMF:27.3.E6
No description defined

    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
    0 references
    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
    Q12233
    Defining formula
    ν ⁡ ( n ) number-of-primes-dividing-nu 𝑛 {\displaystyle{\displaystyle\nu\left(\NVar{n}\right)}}
    xml-id
    C27.S2.SS1.p1.m6abdec
    0 references
    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1edec
    0 references
    Q12235
    Defining formula
    p , p 1 , … 𝑝 subscript 𝑝 1 … {\displaystyle{\displaystyle p,p_{1},\ldots}}
    xml-id
    C27.S1.XMD5.m1cdec
    0 references
    Q12244
    Defining formula
    a r subscript 𝑎 𝑟 {\displaystyle{\displaystyle a_{r}}}
    xml-id
    C27.S2.XMD1.m1bdec
    0 references
     
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