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Show that $\sum \frac{\mu(n) \ln(n)}{n}=-1$

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#number-theory #mobius-function
88
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Calculate values of Möbius function

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#combinatorics #mobius-function
62
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The image of a Möbius transformation

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#complex-analysis #geometry #complex-numbers #mobius-transformation #mobius-function
186
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Count pairwise coprime triples such that the maximum number of the triple is not greater than N

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#combinatorics #number-theory #graph-theory #mobius-function #mobius-inversion
197
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Prove that $\sum_{d|n}\mu(d)\log^m d=0$

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#number-theory #prime-numbers #analytic-number-theory #arithmetic-functions #mobius-function
494
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Product form of Mobius Inversion formula: $g(n)=\prod_{d|n}f(d)^{a(n/d)}\iff f(n)=\prod_{d|n} g(d)^{b(n/d)}$

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#number-theory #analytic-number-theory #arithmetic-functions #mobius-function #mobius-inversion
91
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Need help with finding Dirichlet generating function

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#number-theory #generating-functions #dirichlet-series #mobius-function
160
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$\varphi(x,n)=\sum_{d|n}\mu(d)\left\lfloor\frac xd\right\rfloor$ and $\sum_{d|n}\varphi\left(\frac xd,\frac nd\right)=\lfloor x\rfloor$

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#number-theory #analytic-number-theory #arithmetic-functions #mobius-function #mobius-inversion
110
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Perron's formula application - zeros of $L(s,\chi )$

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#number-theory #analytic-number-theory #complex-integration #dirichlet-series #mobius-function
382
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Möbius inversion and Möbius function as sum of cosines

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#number-theory #contest-math #analytic-number-theory #mobius-function #mobius-inversion
265
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Prove this generalization of Möbius inversion formula

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#number-theory #elementary-number-theory #complex-numbers #mobius-function #mobius-inversion
40
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Proving that $\sum_{k\le x}\frac{k}{\varphi(k)}=Ax+O(\log x)$

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#number-theory #asymptotics #totient-function #mobius-function
119
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Definition of the Möbius function from Vinogradov's book

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#number-theory #mobius-function
89
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Product version of Möbius Inversion formula

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#elementary-number-theory #mobius-function #mobius-inversion
31
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Prove the sum of nth complex primitve roots of unity is $\mu(n)$

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#number-theory #solution-verification #proof-writing #roots-of-unity #mobius-function

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