Question

Can this bound for the abundancy index of $n$ be improved, given that $q^k n^2$ is an odd perfect number with $k=1$?

score 259 · Answer 1 · 2018-10-23 09:18:43

259

Views

Can this bound for the abundancy index of $n$ be improved, given that $q^k n^2$ is an odd perfect number with $k=1$?

Published on 23 Oct 2018 - 9:18

score 149 · Answer 2 · 2018-10-27 01:12:20

149

Views

Asymptotic formula for $\sum_{an+b\le x}\sigma(an+b)$

Published on 27 Oct 2018 - 1:12

score 45 · Answer 3 · 2026-03-25 03:02:38

45

Views

Is comparing real and complex values within Robin's Inequality legal? And how would we?

Published on 25 Mar 2026 - 3:02

score 173 · Answer 4 · 2018-10-30 04:22:14

173

Views

If $x$ and $y$ are solitary numbers satisfying $\gcd(x,y)=1$, under what conditions does it follow that $xy$ is also solitary?

Published on 30 Oct 2018 - 4:22

score 86 · Answer 5 · 2018-10-31 01:23:58

86

Views

The asymptotic behavior of $\sum_{n=1}^x\sigma_a(n)\sigma_b(n)$

Published on 31 Oct 2018 - 1:23

score 313 · Answer 6 · 2018-11-04 01:04:17

313

Views

On $\phi(n) \sigma(n)$ being a square.

Published on 04 Nov 2018 - 1:04

score 258 · Answer 7 · 2018-11-04 18:56:26

258

Views

For what $k\in \mathbb{C}$ do we have $\lim_{x\to\infty}\frac{1}{x^{k+1}}\sum_{n=1}^x \sigma_k(n)=\frac{\zeta(k+1)}{k+1}$?

Published on 04 Nov 2018 - 18:56

score 696 · Answer 8 · 2018-11-08 14:57:54

696

Views

Degree of a canonical divisor on a compact Riemann surface

Published on 08 Nov 2018 - 14:57

score 282 · Answer 9 · 2018-11-19 20:47:35

282

Views

An anomaly regarding the sum of all divisors that is square-free

Published on 19 Nov 2018 - 20:47

score 101 · Answer 10 · 2026-02-22 23:12:31

101

Views

The sum of all divisors of $N$ is a 2 potency iff $N$ is a product of different Mersenne primes

Published on 22 Feb 2026 - 23:12

score 399 · Answer 11 · 2018-11-24 17:34:42

399

Views

Asymptotic behavior $\sum_{n=1}^x\phi_k(n)$, a variant of Euler's Totient function

Published on 24 Nov 2018 - 17:34

score 79 · Answer 12 · 2026-03-22 11:13:05

79

Views

A functional ecuation using divizors

Published on 22 Mar 2026 - 11:13

score 102 · Answer 13 · 2018-11-26 15:02:29

102

Views

A question regarding a paper of Ochem and Rao about the radical of an odd perfect number

Published on 26 Nov 2018 - 15:02

score 376 · Answer 14 · 2018-11-27 14:46:11

376

Views

A proof of $\sum\limits_{d|n} \sigma(d) = n \sum\limits_{d|n} {\tau(d) \over d}$

Published on 27 Nov 2018 - 14:46

score 76 · Answer 15 · 2018-11-28 14:47:56

76

Views

What proportion of the positive integers satisfies $\gcd(n^2,\sigma(n^2))>\sigma(n)$, where $\sigma$ is the sum-of-divisors function?

Published on 28 Nov 2018 - 14:47

List Question

Can this bound for the abundancy index of $n$ be improved, given that $q^k n^2$ is an odd perfect number with $k=1$?

Asymptotic formula for $\sum_{an+b\le x}\sigma(an+b)$

Is comparing real and complex values within Robin's Inequality legal? And how would we?

If $x$ and $y$ are solitary numbers satisfying $\gcd(x,y)=1$, under what conditions does it follow that $xy$ is also solitary?

The asymptotic behavior of $\sum_{n=1}^x\sigma_a(n)\sigma_b(n)$

On $\phi(n) \sigma(n)$ being a square.

For what $k\in \mathbb{C}$ do we have $\lim_{x\to\infty}\frac{1}{x^{k+1}}\sum_{n=1}^x \sigma_k(n)=\frac{\zeta(k+1)}{k+1}$?

Degree of a canonical divisor on a compact Riemann surface

An anomaly regarding the sum of all divisors that is square-free

The sum of all divisors of $N$ is a 2 potency iff $N$ is a product of different Mersenne primes

Asymptotic behavior $\sum_{n=1}^x\phi_k(n)$, a variant of Euler's Totient function

A functional ecuation using divizors

A question regarding a paper of Ochem and Rao about the radical of an odd perfect number

A proof of $\sum\limits_{d|n} \sigma(d) = n \sum\limits_{d|n} {\tau(d) \over d}$

What proportion of the positive integers satisfies $\gcd(n^2,\sigma(n^2))>\sigma(n)$, where $\sigma$ is the sum-of-divisors function?

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