List questions from mobius-inversion

Published on 05 Aug 2016 - 23:39

507

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On Mertens function as $2 \sum_{k=1}^{N} \sum_{n=1}^{\infty}\frac{\mu(n)}{n} \sum_{m=1}^{\infty}\frac{(\mu(k))^{nm}}{m2^{nm}} $

Published on 06 Aug 2016 - 0:23

221

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Mobius inversion formula

Published on 22 Aug 2016 - 11:05

183

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Bernoulli numbers, primes, integers and the Möbius function

Published on 23 Feb 2026 - 5:38

263

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Evaluate $\int_0^1 \frac{\log(1-z)\log(1-z^3)}{z^2}dz$

Published on 02 Nov 2016 - 14:30

237

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Evaluate $\int_0^\infty\left\{ \frac{1}{t} \right\}^{kn}t^{s-1}dt$ for positive integers $n,k$ and $0<\Re s<1$

Published on 04 Nov 2016 - 10:05

857

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Number of relatively prime pairs in a range

Published on 09 Nov 2016 - 7:31

268

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Proving Mobius formula for cyclotomic polynomials without using $x^{n} - 1 = \prod_{d \mid n} \Phi_d(x)$

Published on 10 Nov 2016 - 18:27

85

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Prove by strong induction that if $\sum_{d\mid n} f(d) =F(n)$, and $F(n)$ is multiplative, then so is $f(n)$

Published on 24 Nov 2016 - 11:15

109

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Möbius Inversion with Additional Term

Published on 26 Nov 2016 - 10:28

1k

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show that $ \sum_{p \leq x} \log p \big( \log x - \log p\big) = O(x) $

Published on 02 Dec 2016 - 22:51

67

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Proving non-negativity of möbius inversion of set function

Published on 09 Dec 2016 - 15:29

124

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On the behaviour of $\sum_{\substack{n\leq x\\(n,k)=1}}\frac{1}{\sqrt[\alpha]{n}}$

Published on 19 Dec 2016 - 8:50

804

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Invert: $\sum\limits_{d|n} \mu(d) \lambda(d)=2^{\omega(n)}$

Published on 25 Mar 2026 - 1:21

199

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If $a$ is the arithmetic function with $\sum_{d\mid n}a(d)=2^n$, then $n\mid a(n)$

Published on 13 Jan 2017 - 17:55

List Question

What's about $\sum_{n=1}^\infty\frac{\mu(n)}{n}r^n,$ when $0<r<1$?

On Mertens function as $2 \sum_{k=1}^{N} \sum_{n=1}^{\infty}\frac{\mu(n)}{n} \sum_{m=1}^{\infty}\frac{(\mu(k))^{nm}}{m2^{nm}} $

Mobius inversion formula

Bernoulli numbers, primes, integers and the Möbius function

Evaluate $\int_0^1 \frac{\log(1-z)\log(1-z^3)}{z^2}dz$

Evaluate $\int_0^\infty\left\{ \frac{1}{t} \right\}^{kn}t^{s-1}dt$ for positive integers $n,k$ and $0<\Re s<1$

Number of relatively prime pairs in a range

Proving Mobius formula for cyclotomic polynomials without using $x^{n} - 1 = \prod_{d \mid n} \Phi_d(x)$

Prove by strong induction that if $\sum_{d\mid n} f(d) =F(n)$, and $F(n)$ is multiplative, then so is $f(n)$

Möbius Inversion with Additional Term

show that $ \sum_{p \leq x} \log p \big( \log x - \log p\big) = O(x) $

Proving non-negativity of möbius inversion of set function

On the behaviour of $\sum_{\substack{n\leq x\\(n,k)=1}}\frac{1}{\sqrt[\alpha]{n}}$

Invert: $\sum\limits_{d|n} \mu(d) \lambda(d)=2^{\omega(n)}$

If $a$ is the arithmetic function with $\sum_{d\mid n}a(d)=2^n$, then $n\mid a(n)$

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