Question

What proportion of the natural numbers satisfies the following inequality?

score 230 · Answer 1 · 2018-05-03 15:18:57

230

Views

What proportion of the natural numbers satisfies the following inequality?

Published on 03 May 2018 - 15:18

score 26 · Answer 2 · 2018-05-08 10:48:12

26

Views

Questions regarding equations that involve arithmetic functions, and odd integers being deficient or perfect

Published on 08 May 2018 - 10:48

score 53 · Answer 3 · 2026-03-22 20:11:14

53

Views

Does $D(n)$ always depend on $\gcd(n,\sigma(n))$ when $\sigma(N)=aN+b$, $N=xn$, and $n$ is a square?

Published on 22 Mar 2026 - 20:11

score 1.8k · Answer 4 · 2026-03-21 19:29:06

1.8k

Views

Even Descartes numbers

Published on 21 Mar 2026 - 19:29

score 200 · Answer 5 · 2026-03-22 18:46:26

200

Views

Do odd numbers $n$ satisfying $\gcd(n, \sigma(n)) > \sqrt{n}$ have a special form?

Published on 22 Mar 2026 - 18:46

score 36 · Answer 6 · 2018-05-22 10:55:50

36

Views

An artificious equation that is satisfied by even perfect numbers, and a related conjecture

Published on 22 May 2018 - 10:55

score 74 · Answer 7 · 2026-03-17 18:00:15

74

Views

Would like to get numerical (lower [and upper?]) bounds for $p$

Published on 17 Mar 2026 - 18:00

score 266 · Answer 8 · 2018-05-29 17:56:44

266

Views

Odd abundant numbers and the condition $\sqrt{n^2+12n\sigma(n)}\in\mathbb{Z}_{\geq 1}$

Published on 29 May 2018 - 17:56

score 160 · Answer 9 · 2018-06-01 20:20:24

160

Views

On prime-perfect numbers and the equation $\frac{\varphi(n)}{n}=\frac{\varphi(\operatorname{rad}(n))}{\operatorname{rad}(\sigma(n))}$

Published on 01 Jun 2018 - 20:20

score 249 · Answer 10 · 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 77 · Answer 11 · 2018-06-05 15:05:49

77

Views

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

Published on 05 Jun 2018 - 15:05

score 89 · Answer 12 · 2026-03-20 10:59:18

89

Views

$\sum\limits_{\mathbb{d|n}}{f(d)}=\sum\limits_{\mathbb{d|n}}{g(d)}\implies f(n)=g(n)?$

Published on 20 Mar 2026 - 10:59

score 150 · Answer 13 · 2018-06-07 10:03:45

150

Views

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

Published on 07 Jun 2018 - 10:03

score 216 · Answer 14 · 2018-06-08 09:17:00

216

Views

On $\text{Lower bound}\leq \operatorname{rad}(n)$, where $n$ is an odd perfect number: reference request or what work can be done about it

Published on 08 Jun 2018 - 9:17

score 687 · Answer 15 · 2026-03-17 09:52:05

687

Views

A conjecture regarding odd perfect numbers

Published on 17 Mar 2026 - 9:52

List Question

What proportion of the natural numbers satisfies the following inequality?

Questions regarding equations that involve arithmetic functions, and odd integers being deficient or perfect

Does $D(n)$ always depend on $\gcd(n,\sigma(n))$ when $\sigma(N)=aN+b$, $N=xn$, and $n$ is a square?

Even Descartes numbers

Do odd numbers $n$ satisfying $\gcd(n, \sigma(n)) > \sqrt{n}$ have a special form?

An artificious equation that is satisfied by even perfect numbers, and a related conjecture

Would like to get numerical (lower [and upper?]) bounds for $p$

Odd abundant numbers and the condition $\sqrt{n^2+12n\sigma(n)}\in\mathbb{Z}_{\geq 1}$

On prime-perfect numbers and the equation $\frac{\varphi(n)}{n}=\frac{\varphi(\operatorname{rad}(n))}{\operatorname{rad}(\sigma(n))}$

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

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

$\sum\limits_{\mathbb{d|n}}{f(d)}=\sum\limits_{\mathbb{d|n}}{g(d)}\implies f(n)=g(n)?$

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

On $\text{Lower bound}\leq \operatorname{rad}(n)$, where $n$ is an odd perfect number: reference request or what work can be done about it

A conjecture regarding odd perfect numbers

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