Question

Iterations of the radical of an integer

score 186 · Answer 1 · 2026-03-25 09:32:06

186

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Iterations of the radical of an integer

Published on 25 Mar 2026 - 9:32

score 311 · Answer 2 · 2026-03-27 18:26:38

311

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

Published on 27 Mar 2026 - 18:26

score 190 · Answer 3 · 2026-03-21 21:00:14

190

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

Published on 21 Mar 2026 - 21:00

score 126 · Answer 4 · 2018-06-01 16:05:34

126

Views

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

Published on 01 Jun 2018 - 16:05

score 191 · Answer 5 · 2026-03-25 01:21:46

191

Views

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

Published on 25 Mar 2026 - 1:21

score 64 · Answer 6 · 2026-03-25 17:59:55

64

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

Published on 25 Mar 2026 - 17:59

score 249 · Answer 7 · 2026-03-22 18:02:33

249

Views

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

Published on 22 Mar 2026 - 18:02

score 243 · Answer 8 · 2026-03-25 11:16:37

243

Views

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

Published on 25 Mar 2026 - 11:16

score 42 · Answer 9 · 2018-06-04 16:10:20

42

Views

Contribution of Halphen to the PNT

Published on 04 Jun 2018 - 16:10

score 116 · Answer 10 · 2026-03-26 20:41:54

116

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 26 Mar 2026 - 20:41

score 78 · Answer 11 · 2026-03-25 04:42:37

78

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

Published on 25 Mar 2026 - 4:42

score 51 · Answer 12 · 2026-03-27 20:22:28

51

Views

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

Published on 27 Mar 2026 - 20:22

score 148 · Answer 13 · 2026-03-24 23:44:44

148

Views

What is the difference between infinite product and regularized product?

Published on 24 Mar 2026 - 23:44

score 243 · Answer 14 · 2026-03-27 20:21:23

243

Views

Basic question about the zeros of Riemann Zeta Function

Published on 27 Mar 2026 - 20:21

score 151 · Answer 15 · 2026-03-25 04:42:50

151

Views

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

Published on 25 Mar 2026 - 4:42

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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