DLMF:27.14.E7 (Q8106): Difference between revisions

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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
 
test:

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
Property / Symbols used
 
Property / Symbols used: Q12187 / rank
 
Normal rank
Property / Symbols used: Q12187 / qualifier
 
test:

p ( n ) partition-function 𝑛 {\displaystyle{\displaystyle p\left(\NVar{n}\right)}}

\npartitions[]@{\NVar{n}}
Property / Symbols used: Q12187 / qualifier
 
xml-id: C26.S2.Px4.p2.m5abdec
Property / Symbols used
 
Property / Symbols used: Q12238 / rank
 
Normal rank
Property / Symbols used: Q12238 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12238 / qualifier
 
xml-id: C27.S1.XMD2.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12234 / rank
 
Normal rank
Property / Symbols used: Q12234 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12234 / qualifier
 
xml-id: C27.S1.XMD4.m1cdec

Latest revision as of 13:30, 2 January 2020

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DLMF:27.14.E7
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    Statements

    n p ( n ) = k = 1 n σ 1 ( k ) p ( n - k ) , 𝑛 partition-function 𝑛 superscript subscript 𝑘 1 𝑛 divisor-sigma 1 𝑘 partition-function 𝑛 𝑘 {\displaystyle{\displaystyle np\left(n\right)=\sum_{k=1}^{n}\sigma_{1}\left(k% \right)p\left(n-k\right),}}
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    σ α ( n ) divisor-sigma 𝛼 𝑛 {\displaystyle{\displaystyle\sigma_{\NVar{\alpha}}\left(\NVar{n}\right)}}
    C27.S2.E10.m2adec
    0 references
    p ( n ) partition-function 𝑛 {\displaystyle{\displaystyle p\left(\NVar{n}\right)}}
    C26.S2.Px4.p2.m5abdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C27.S1.XMD2.m1cdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C27.S1.XMD4.m1cdec
    0 references