Question

Iterations of the radical of an integer

score 189 · Answer 1 · 2026-05-10 20:53:08

189

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Iterations of the radical of an integer

Published on 10 May 2026 - 20:53

score 313 · Answer 2 · 2026-04-16 12:11:26

313

Views

This article claims to prove that all $\zeta(2n+1)$ for integer $n>0$ are irrational. Is it correct?

Published on 16 Apr 2026 - 12:11

score 191 · Answer 3 · 2026-04-09 03:41:15

191

Views

Convergence of $\sum_{k=1}^\infty\frac{\operatorname{rad}(k!)}{\operatorname{lcm}(1,2,\ldots,k)}$

Published on 09 Apr 2026 - 3:41

score 129 · Answer 4 · 2026-04-16 12:51:27

129

Views

On sum of arithmetic functions $\mu(n) / \phi(n)$ and $\mu(n) \log(n) / \phi(n)$.

Published on 16 Apr 2026 - 12:51

score 194 · Answer 5 · 2026-05-10 14:04:22

194

Views

Dirichlet series generated by $\mu(n) / \phi(n)$

Published on 10 May 2026 - 14:04

score 69 · Answer 6 · 2026-05-13 19:12:42

69

Views

On numbers of the form $\pm x^2\pm N_k$, with $x\geq 1$ integer and $N_k$ denoting primorials

Published on 13 May 2026 - 19:12

score 256 · Answer 7 · 2026-05-10 18:36:21

256

Views

Has $\sigma\left(\sigma_0(n)^4\right)=n$ infinitely many solutions?

Published on 10 May 2026 - 18:36

score 246 · Answer 8 · 2026-05-11 09:35:32

246

Views

Square-free integers in the sequence $n^{\operatorname{rad}(n)}+\operatorname{rad}(n)+1$

Published on 11 May 2026 - 9:35

score 45 · Answer 9 · 2026-04-14 03:14:56

45

Views

Contribution of Halphen to the PNT

Published on 14 Apr 2026 - 3:14

score 118 · Answer 10 · 2026-04-15 08:15:12

118

Views

Asymptotic Expansion of $\frac{1}{2\pi i} \int_{c-i\infty}^{c+i\infty}\frac{x^{s+1}}{s(s+1)}(1-2^{-s})\zeta^2(s)ds$

Published on 15 Apr 2026 - 8:15

score 81 · Answer 11 · 2026-05-10 15:10:27

81

Views

On the equation $\sigma(m)=105k$ over odd integers $m\geq 1$, and the deficiency of its solutions

Published on 10 May 2026 - 15:10

score 53 · Answer 12 · 2026-04-16 05:06:04

53

Views

Zeroes of $L(s,q)=\prod_{\chi(\text{mod}\ q)}L(s,\chi)$ in a rectengle

Published on 16 Apr 2026 - 5:06

score 151 · Answer 13 · 2026-05-10 14:04:58

151

Views

What is the difference between infinite product and regularized product?

Published on 10 May 2026 - 14:04

score 245 · Answer 14 · 2026-04-08 17:03:29

245

Views

Basic question about the zeros of Riemann Zeta Function

Published on 08 Apr 2026 - 17:03

score 153 · Answer 15 · 2026-05-10 15:09:53

153

Views

Estimation of the number of solutions for the equation $\sigma(\varphi(n))=\sigma(\operatorname{rad}(n))$

Published on 10 May 2026 - 15:09

List Question

Iterations of the radical of an integer

This article claims to prove that all $\zeta(2n+1)$ for integer $n>0$ are irrational. Is it correct?

Convergence of $\sum_{k=1}^\infty\frac{\operatorname{rad}(k!)}{\operatorname{lcm}(1,2,\ldots,k)}$

On sum of arithmetic functions $\mu(n) / \phi(n)$ and $\mu(n) \log(n) / \phi(n)$.

Dirichlet series generated by $\mu(n) / \phi(n)$

On numbers of the form $\pm x^2\pm N_k$, with $x\geq 1$ integer and $N_k$ denoting primorials

Has $\sigma\left(\sigma_0(n)^4\right)=n$ infinitely many solutions?

Square-free integers in the sequence $n^{\operatorname{rad}(n)}+\operatorname{rad}(n)+1$

Contribution of Halphen to the PNT

Asymptotic Expansion of $\frac{1}{2\pi i} \int_{c-i\infty}^{c+i\infty}\frac{x^{s+1}}{s(s+1)}(1-2^{-s})\zeta^2(s)ds$

On the equation $\sigma(m)=105k$ over odd integers $m\geq 1$, and the deficiency of its solutions

Zeroes of $L(s,q)=\prod_{\chi(\text{mod}\ q)}L(s,\chi)$ in a rectengle

What is the difference between infinite product and regularized product?

Basic question about the zeros of Riemann Zeta Function

Estimation of the number of solutions for the equation $\sigma(\varphi(n))=\sigma(\operatorname{rad}(n))$

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