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Mangoldt function (Definition)

The Mangoldt function $\Lambda$ is defined by

\begin{displaymath}\Lambda (n) = \begin{cases} \ln p, &\text{if $n=p^k$, where $... ...a natural number $\geq 1$}\ 0, &\text{otherwise} \end{cases} \end{displaymath}

The Moebius Inversion Formula leads to the identity $\Lambda (n) = \sum_{d|n} \mu (n/d) \ln d = - \sum_{d|n} \mu (d) \ln d$ .




"Mangoldt function" is owned by KimJ.
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Other names:  von Mangoldt function
Keywords:  number theory
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Cross-references: identity, formula, Moebius inversion
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This is version 5 of Mangoldt function, born on 2001-10-16, modified 2003-03-06.
Object id is 256, canonical name is MangoldtFunction.
Accessed 4950 times total.

Classification:
AMS MSC11A25 (Number theory :: Elementary number theory :: Arithmetic functions; related numbers; inversion formulas)

Pending Errata and Addenda
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Multiplicativity of Mangoldt function by XJamRastafire on 2002-06-13 11:03:45
I have one simple (perhaps not so) question - is Mangoldt function a multiplicative function?
I can't answer this at first glance.
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