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DLMF:27.3.E4 - MaRDI portal

DLMF:27.3.E4 (Q8698)

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DLMF:27.3.E4
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    Statements

    DLMF defining formula
    J k ⁑ ( n ) = n k ⁒ ∏ p | n ( 1 - p - k ) , Jordan-J π‘˜ 𝑛 superscript 𝑛 π‘˜ subscript product divides 𝑝 𝑛 1 superscript 𝑝 π‘˜ {\displaystyle{\displaystyle J_{k}\left(n\right)=n^{k}\prod_{p\mathbin{|}n}(1-% p^{-k}),}}
    0 references
    Symbols used
    Jordan’s function
    DLMF defining formula
    J k ⁑ ( n ) Jordan-J π‘˜ 𝑛 {\displaystyle{\displaystyle J_{\NVar{k}}\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E11.m2adec
    0 references
    positive integer
    DLMF defining formula
    k π‘˜ {\displaystyle{\displaystyle k}}
    xml-id
    C27.S1.XMD2.m1dec
    0 references
    positive integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1cdec
    0 references
    prime numbers
    DLMF defining formula
    p , p 1 , … 𝑝 subscript 𝑝 1 … {\displaystyle{\displaystyle p,p_{1},\ldots}}
    xml-id
    C27.S1.XMD5.m1bdec
    0 references

    Identifiers

     
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