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 · 2026-03-25 14:46:56

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 25 Mar 2026 - 14:46

score 1.4k · Answer 2 · 2026-04-16 20:00:37

1.4k

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

Published on 16 Apr 2026 - 20:00

score 85 · Answer 3 · 2026-04-16 11:19:47

85

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

Published on 16 Apr 2026 - 11:19

score 279 · Answer 4 · 2026-04-14 20:26:05

279

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Generalization of Möbius Inversion

Published on 14 Apr 2026 - 20:26

score 1k · Answer 5 · 2026-04-12 19:36:10

1k

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Fractals and Kleinian groups - Rendering the limit set

Published on 12 Apr 2026 - 19:36

score 94 · Answer 6 · 2026-04-15 07:45:58

94

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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 15 Apr 2026 - 7:45

score 53 · Answer 7 · 2026-03-25 14:46:55

53

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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 25 Mar 2026 - 14:46

score 132 · Answer 8 · 2026-03-25 14:39:18

132

Views

Applications of the mobius inversion in algebraic or arithmetic geometry

Published on 25 Mar 2026 - 14:39

score 203 · Answer 9 · 2026-03-25 14:39:19

203

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Proof of the dual Möbius Inversion Formula

Published on 25 Mar 2026 - 14:39

score 43 · Answer 10 · 2026-03-25 14:46:54

43

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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 25 Mar 2026 - 14:46

score 61 · Answer 11 · 2026-04-30 11:18:46

61

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Problems about inversion map

Published on 30 Apr 2026 - 11:18

score 92 · Answer 12 · 2026-03-25 14:39:53

92

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Partial Möbius convolutions

Published on 25 Mar 2026 - 14:39

score 175 · Answer 13 · 2026-03-25 14:39:49

175

Views

Bounding a partial sum with Möbius inversion formula

Published on 25 Mar 2026 - 14:39

score 59 · Answer 14 · 2026-03-25 14:39:08

59

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

Published on 25 Mar 2026 - 14:39

score 44 · Answer 15 · 2026-04-09 07:32:33

44

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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 09 Apr 2026 - 7:32

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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