Question

Showing $\sum_{d\mid n} \mu(d)\tau(n/d)=1$ and $\sum_{d\mid n} \mu(d)\tau(d)=(-1)^r$

score 2k · Answer 1 · 2026-03-21 23:23:10

2k

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Showing $\sum_{d\mid n} \mu(d)\tau(n/d)=1$ and $\sum_{d\mid n} \mu(d)\tau(d)=(-1)^r$

Published on 21 Mar 2026 - 23:23

score 1.4k · Answer 2 · 2017-01-21 19:21:17

1.4k

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Prove that $\sum_{d|n, d \geq 1}{|\mu(d)|} = 2^{\omega(n)}$

Published on 21 Jan 2017 - 19:21

score 82 · Answer 3 · 2017-01-27 08:34:42

82

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Why does $N$ divide $\sum_{d|N} p^{md} \mu\bigg(\frac{N}{d}\bigg)$?

Published on 27 Jan 2017 - 8:34

score 277 · Answer 4 · 2017-02-10 10:30:48

277

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Generalization of Möbius Inversion

Published on 10 Feb 2017 - 10:30

score 1k · Answer 5 · 2017-03-17 20:54:24

1k

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Fractals and Kleinian groups - Rendering the limit set

Published on 17 Mar 2017 - 20:54

score 91 · Answer 6 · 2017-04-04 01:00:16

91

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Prove $\sum_{d|n} \frac{\Phi(d)}{d} = \prod_{i=1}^r (1 + a_i - \frac{a_i}{p_i})$

Published on 04 Apr 2017 - 1:00

score 52 · Answer 7 · 2023-02-16 16:45:36

52

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Is the set of divisor indicator functions at $x^2 - 1$: $B' = \{(d \mid x^2 - 1) : d \in \Bbb{N}\}$ a $\Bbb{Z}$-linearly independent set?

Published on 16 Feb 2023 - 16:45

score 131 · Answer 8 · 2023-05-05 23:20:51

131

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Applications of the mobius inversion in algebraic or arithmetic geometry

Published on 05 May 2023 - 23:20

score 202 · Answer 9 · 2023-06-02 21:13:10

202

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Proof of the dual Möbius Inversion Formula

Published on 02 Jun 2023 - 21:13

score 42 · Answer 10 · 2023-06-23 11:32:48

42

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Prime numbers as zeros of polynomials from the determinant of the form $P(x,N)=|\log(x) \gcd (n,k)-\phi (n)\log(\gcd (n,k))|$

Published on 23 Jun 2023 - 11:32

score 59 · Answer 11 · 2023-08-05 17:26:40

59

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Problems about inversion map

Published on 05 Aug 2023 - 17:26

score 91 · Answer 12 · 2023-10-07 12:10:42

91

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Partial Möbius convolutions

Published on 07 Oct 2023 - 12:10

score 174 · Answer 13 · 2023-11-06 11:51:46

174

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Bounding a partial sum with Möbius inversion formula

Published on 06 Nov 2023 - 11:51

score 58 · Answer 14 · 2023-11-13 00:08:16

58

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Möbius inversion formula and $\sum_{k\leq n} \frac{\mu(k)}{k}$

Published on 13 Nov 2023 - 0:08

score 43 · Answer 15 · 2026-02-23 01:23:46

43

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Prove the Fourier coefficients $c_S$ of $f\colon\mathbb{F}_2^n\to\mathbb{F_2}$ is $\sum_{\operatorname{supp}(x)\subseteq S}f(x)$

Published on 23 Feb 2026 - 1:23

List Question

Showing $\sum_{d\mid n} \mu(d)\tau(n/d)=1$ and $\sum_{d\mid n} \mu(d)\tau(d)=(-1)^r$

Prove that $\sum_{d|n, d \geq 1}{|\mu(d)|} = 2^{\omega(n)}$

Why does $N$ divide $\sum_{d|N} p^{md} \mu\bigg(\frac{N}{d}\bigg)$?

Generalization of Möbius Inversion

Fractals and Kleinian groups - Rendering the limit set

Prove $\sum_{d|n} \frac{\Phi(d)}{d} = \prod_{i=1}^r (1 + a_i - \frac{a_i}{p_i})$

Is the set of divisor indicator functions at $x^2 - 1$: $B' = \{(d \mid x^2 - 1) : d \in \Bbb{N}\}$ a $\Bbb{Z}$-linearly independent set?

Applications of the mobius inversion in algebraic or arithmetic geometry

Proof of the dual Möbius Inversion Formula

Prime numbers as zeros of polynomials from the determinant of the form $P(x,N)=|\log(x) \gcd (n,k)-\phi (n)\log(\gcd (n,k))|$

Problems about inversion map

Partial Möbius convolutions

Bounding a partial sum with Möbius inversion formula

Möbius inversion formula and $\sum_{k\leq n} \frac{\mu(k)}{k}$

Prove the Fourier coefficients $c_S$ of $f\colon\mathbb{F}_2^n\to\mathbb{F_2}$ is $\sum_{\operatorname{supp}(x)\subseteq S}f(x)$

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