DLMF:27.5.E8 (Q8032)

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DLMF:27.5.E8
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    g ( n ) = d | n f ( d ) f ( n ) = d | n ( g ( n d ) ) μ ( d ) . 𝑔 𝑛 subscript product divides 𝑑 𝑛 𝑓 𝑑 𝑓 𝑛 subscript product divides 𝑑 𝑛 superscript 𝑔 𝑛 𝑑 Moebius-mu 𝑑 {\displaystyle{\displaystyle g(n)=\prod_{d\mathbin{|}n}f(d)\Longleftrightarrow f% (n)=\prod_{d\mathbin{|}n}\left(g\left(\frac{n}{d}\right)\right)^{\mu\left(d% \right)}.}}
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    DLMF:27.5.E8
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    μ ( n ) Moebius-mu 𝑛 {\displaystyle{\displaystyle\mu\left(\NVar{n}\right)}}
    C27.S2.E12.m2afdec
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    d 𝑑 {\displaystyle{\displaystyle d}}
    C27.S1.XMD1.m1edec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C27.S1.XMD4.m1fdec
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