Question

Prove $\sum\limits_{n \leq x, \gcd(n,k)=1}\frac{1}{n} = \sum\limits_{d|k}\frac{\mu}{d}\log x + O(1)$

score 496 · Answer 1 · 2026-03-27 06:12:34

496

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Prove $\sum\limits_{n \leq x, \gcd(n,k)=1}\frac{1}{n} = \sum\limits_{d|k}\frac{\mu}{d}\log x + O(1)$

Published on 27 Mar 2026 - 6:12

score 77 · Answer 2 · 2026-04-13 00:10:25

77

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Step in the proof of the Montgomery and Vaughan generalisation of Hilbert Inequality

Published on 13 Apr 2026 - 0:10

score 144 · Answer 3 · 2026-04-15 06:27:03

144

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Step in Proof of Montgomery and Vaughan generalisation of Hilbert Inequality part 2

Published on 15 Apr 2026 - 6:27

score 377 · Answer 4 · 2026-04-16 14:49:58

377

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Convergence of an integral involving the radical of an integer versus the convergence of $\int_2^\infty\frac{dx}{x(\log x)^2}$

Published on 16 Apr 2026 - 14:49

score 177 · Answer 5 · 2026-04-14 18:04:51

177

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On the number of solutions of a type of diophantine equation

Published on 14 Apr 2026 - 18:04

score 180 · Answer 6 · 2026-04-12 18:59:10

180

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Can we prove Prime number theorem by prime factorization?

Published on 12 Apr 2026 - 18:59

score 39 · Answer 7 · 2026-03-26 02:56:02

39

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Unable to understand the meaning of $\mathcal{B\pmod t}$

Published on 26 Mar 2026 - 2:56

score 203 · Answer 8 · 2026-03-26 00:53:44

203

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On arithmetic functions whose Dirichlet series has a special kind of abscissa of absolute convergence

Published on 26 Mar 2026 - 0:53

score 233 · Answer 9 · 2026-04-16 10:18:24

233

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Looking for the closed form of $\sum_{n=1}^{\infty}{\zeta(2n+1)\over (2n+1)2^{4n}}$

Published on 16 Apr 2026 - 10:18

score 220 · Answer 10 · 2026-04-15 06:03:09

220

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On integer values which are attained by $n/\pi(n)$ only once

Published on 15 Apr 2026 - 6:03

score 232 · Answer 11 · 2026-03-25 15:49:47

232

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A fun fact relating to Goldbach Conjecture

Published on 25 Mar 2026 - 15:49

score 211 · Answer 12 · 2026-03-25 15:52:43

211

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The $\operatorname{rad}(3x+1)$ problem, where $\operatorname{rad}(n)$ is the radical of an integer

Published on 25 Mar 2026 - 15:52

score 230 · Answer 13 · 2026-03-27 06:09:15

230

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On $\int_1^\infty \left(\sum_{1\leq k\leq t}\frac{\mu(k)}{k}\right)\log \left(\frac{1-e^{\frac{2\pi i}{t}}}{1-e^{\frac{-2\pi i}{t}}}\right)dt$

Published on 27 Mar 2026 - 6:09

score 79 · Answer 14 · 2026-04-14 05:07:26

79

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$\sum c_nn^{-s_0}$ converges implies $\sum c_nn^{-s}$ cannot have a pole in the line $\Re{s}=\sigma_0$

Published on 14 Apr 2026 - 5:07

score 330 · Answer 15 · 2026-04-20 08:27:57

330

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Looking for a mild introduction to probabilistic methods.

Published on 20 Apr 2026 - 8:27

List Question

Prove $\sum\limits_{n \leq x, \gcd(n,k)=1}\frac{1}{n} = \sum\limits_{d|k}\frac{\mu}{d}\log x + O(1)$

Step in the proof of the Montgomery and Vaughan generalisation of Hilbert Inequality

Step in Proof of Montgomery and Vaughan generalisation of Hilbert Inequality part 2

Convergence of an integral involving the radical of an integer versus the convergence of $\int_2^\infty\frac{dx}{x(\log x)^2}$

On the number of solutions of a type of diophantine equation

Can we prove Prime number theorem by prime factorization?

Unable to understand the meaning of $\mathcal{B\pmod t}$

On arithmetic functions whose Dirichlet series has a special kind of abscissa of absolute convergence

Looking for the closed form of $\sum_{n=1}^{\infty}{\zeta(2n+1)\over (2n+1)2^{4n}}$

On integer values which are attained by $n/\pi(n)$ only once

A fun fact relating to Goldbach Conjecture

The $\operatorname{rad}(3x+1)$ problem, where $\operatorname{rad}(n)$ is the radical of an integer

On $\int_1^\infty \left(\sum_{1\leq k\leq t}\frac{\mu(k)}{k}\right)\log \left(\frac{1-e^{\frac{2\pi i}{t}}}{1-e^{\frac{-2\pi i}{t}}}\right)dt$

$\sum c_nn^{-s_0}$ converges implies $\sum c_nn^{-s}$ cannot have a pole in the line $\Re{s}=\sigma_0$

Looking for a mild introduction to probabilistic methods.

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