List questions from arithmetic-functions

Published on 25 Mar 2026 - 17:17

100

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Hints to compute if exists $\lim_{n\to\infty}\sum_{k=1}^n\sigma(k^2)/\sum_{k=1}^n\sigma(k)$, which $\sigma(n)=\sum_{d\mid n}d$, and other question

Published on 29 Nov 2015 - 11:02

109

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Can be justified this formula for $\zeta(2n+1)$

Published on 09 Dec 2015 - 15:42

71

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How can one show that $f(n)>n$

Published on 10 Dec 2015 - 0:03

104

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What about $\lim_{n\to\infty}\frac{\sum_{k=1}^n s_k\mu(k)}{n}$, for the zeros of Dirichlet eta function $s_k=1+\frac{2\pi k}{\log 2}i$ with $k\geq 1$?

Published on 12 Dec 2015 - 17:17

134

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What inequalities similar Lagarias' statement are easy to prove?

Published on 07 Jan 2016 - 18:59

97

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Prove that $τ(m^n)$ and $n$ are coprime $(m,n ∈ N^+)$

Published on 27 Mar 2026 - 3:43

228

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An identity involving $[\sigma(n)]^2$

Published on 12 Jan 2016 - 5:09

52

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How is countably infinite addition defined

Published on 13 Jan 2016 - 16:28

65

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$Φ_n$ is Euler group, $n> 2$ is an integer, and $m$ the number of solutions of the equation $x^2 = 1$ in the ring $Z_n$.

Published on 17 Jan 2016 - 14:37

60

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Two questions about pseudo equidistributed sequences modulo 1

Published on 25 Mar 2026 - 19:13

186

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Can you prove this identity involving the divisor sum function?

Published on 08 Feb 2016 - 21:42

140

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What about $\sum_{\substack{2\leq n\leq y,\text{n prime}}}n\log\log n$ when $y=[x]\to\infty$?

Published on 11 Feb 2016 - 7:27

250

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Vaughan's identity, a didactic example

Published on 27 Mar 2026 - 0:55

378

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Exploring the Dirichlet series of the sum of remainder function

Published on 26 Mar 2026 - 12:07

List Question

On a generalization for $\sum_{d|n}rad(d)\phi(\frac{n}{d})$ and related questions

Hints to compute if exists $\lim_{n\to\infty}\sum_{k=1}^n\sigma(k^2)/\sum_{k=1}^n\sigma(k)$, which $\sigma(n)=\sum_{d\mid n}d$, and other question

Can be justified this formula for $\zeta(2n+1)$

How can one show that $f(n)>n$

What about $\lim_{n\to\infty}\frac{\sum_{k=1}^n s_k\mu(k)}{n}$, for the zeros of Dirichlet eta function $s_k=1+\frac{2\pi k}{\log 2}i$ with $k\geq 1$?

What inequalities similar Lagarias' statement are easy to prove?

Prove that $τ(m^n)$ and $n$ are coprime $(m,n ∈ N^+)$

An identity involving $[\sigma(n)]^2$

How is countably infinite addition defined

$Φ_n$ is Euler group, $n> 2$ is an integer, and $m$ the number of solutions of the equation $x^2 = 1$ in the ring $Z_n$.

Two questions about pseudo equidistributed sequences modulo 1

Can you prove this identity involving the divisor sum function?

What about $\sum_{\substack{2\leq n\leq y,\text{n prime}}}n\log\log n$ when $y=[x]\to\infty$?

Vaughan's identity, a didactic example

Exploring the Dirichlet series of the sum of remainder function

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