User Jose Arnaldo Bebita

16 votes

1 answer

2k views

On J. T. Condict's Senior Thesis on Odd Perfect Numbers

asked Dec 11, 2011 at 4:34

13 votes

2 answers

2k views

Has it been proved that odd perfect numbers cannot be triangular?

asked Mar 25, 2016 at 22:30

9 votes

2 answers

766 views

Is there an odd integer $x < 105$ for which it is known that $x \nmid N$, if $N$ is an odd perfect number?

asked Aug 11, 2014 at 14:58

6 votes

1 answer

2k views

If $N = qn^2$ is an odd perfect number with $\gcd(q,n)=1$, is it possible to have $q + 1 = \sigma(n)$?

asked Feb 4, 2016 at 14:02

6 votes

3 answers

4k views

Re: Mordell's equation $y^2 = x^3 + k$ and perfect numbers

asked Dec 3, 2010 at 19:49

6 votes

0 answers

506 views

Does the equation $\sigma(\sigma(x^2))=2x\sigma(x)$ have any odd solutions?

asked Aug 25, 2020 at 2:33

4 votes

1 answer

1k views

On Sorli's Conjecture Re: OPNs (Circa 2003)

asked Dec 3, 2010 at 18:29

4 votes

1 answer

335 views

If $N = {q^k}{n^2}$ is an odd perfect number given in Eulerian form, is $n$ a square?

asked Dec 27, 2015 at 10:53

4 votes

2 answers

470 views

On the natural density of almost perfect numbers

asked May 14, 2015 at 11:07

3 votes

0 answers

177 views

Looking for an appropriate reference(s) for two conjectures on odd perfect numbers

asked Sep 11, 2016 at 2:40

3 votes

4 answers

1k views

A conjecture regarding odd perfect numbers

asked Sep 19, 2018 at 7:44

3 votes

0 answers

180 views

Does this Theorem 2 from Dandapat et al. imply that $\gcd(\sigma(p^k),\sigma(a^2)) > 1$?

asked Dec 25, 2021 at 16:53

2 votes

2 answers

484 views

On odd perfect numbers $p^k m^2$ with special prime $p$ satisfying $m^2 - p^k = 2^r t$ - Part II

asked Oct 21, 2021 at 9:10

2 votes

2 answers

642 views

On the nearest-square function and the quantity $m^2 - p^k$ where $p^k m^2$ is an odd perfect number

asked Nov 12, 2020 at 7:26

2 votes

0 answers

342 views

On odd perfect numbers and a GCD - Part II

asked Dec 8, 2020 at 5:02

2 votes

1 answer

345 views

On odd perfect numbers $q^k n^2$ satisfying $n^2 - q^k = 2^r t$

asked May 26, 2021 at 5:39

2 votes

0 answers

751 views

Does $n \mid \sigma(n^2)$, if $q^k n^2$ is an odd perfect number?

asked Sep 26, 2021 at 7:13

2 votes

1 answer

137 views

If $p^k m^2$ is an odd perfect number with special prime $p$, then must $m^2 - p^k = s^2 - t^2$ hold for some $s$ and $t$?

asked Feb 15 at 5:19

2 votes

0 answers

116 views

If $n$ is a multiperfect number, then necessarily does one of its prime factors $p$ satisfy $p \parallel n$?

asked Aug 9, 2020 at 2:51

2 votes

1 answer

169 views

Is the asymptotic density of positive integers $n$ satisfying $\gcd(n, \sigma(n^2))=\gcd(n^2, \sigma(n^2))$ equal to zero?

asked Aug 18, 2020 at 4:13

2 votes

1 answer

259 views

On attempting a proof for $r > 1$, if $M = {2^r}{b^2}$ is an even almost perfect number which is not a power of two

asked May 14, 2016 at 2:26

2 votes

0 answers

204 views

On the conjectured nonexistence of even almost perfect numbers (other than powers of two) and odd perfect numbers [closed]

asked Jun 27, 2016 at 12:50

2 votes

1 answer

656 views

Reference Request - Sharp Estimates for a Logarithmic Sum

asked Dec 3, 2010 at 19:23

2 votes

1 answer

332 views

A question on a special type of function

asked Mar 2, 2011 at 5:27

2 votes

1 answer

301 views

What proportion of the positive integers satisfy $I(n) < \frac{2n}{n + 1} \leq I(n^2) < 2$?

asked Sep 9, 2013 at 14:45

2 votes

0 answers

286 views

What are the divisors of $2n^2 - \sigma_{1}(n^2)$ for composite $n$?

asked Oct 1, 2013 at 15:36

2 votes

1 answer

322 views

Reference request: Research done on whether the Euler prime can be the largest factor of an odd perfect number

asked Feb 11, 2015 at 18:51

2 votes

0 answers

487 views

On Descartes / spoof odd perfect numbers

asked Mar 5, 2015 at 3:37

2 votes

1 answer

325 views

Does there exist an integer that is both solitary and almost perfect?

asked Mar 25, 2015 at 10:16

1 vote

2 answers

199 views

What proportion of the positive integers satisfy $I(n^2) < (1 + \frac{1}{n})I(n)$, where $I(x)$ is the abundancy index of $x$?

asked Oct 1, 2013 at 16:42

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59 Questions

On J. T. Condict's Senior Thesis on Odd Perfect Numbers

Has it been proved that odd perfect numbers cannot be triangular?

Is there an odd integer $x < 105$ for which it is known that $x \nmid N$, if $N$ is an odd perfect number?

If $N = qn^2$ is an odd perfect number with $\gcd(q,n)=1$, is it possible to have $q + 1 = \sigma(n)$?

Re: Mordell's equation $y^2 = x^3 + k$ and perfect numbers

Does the equation $\sigma(\sigma(x^2))=2x\sigma(x)$ have any odd solutions?

On Sorli's Conjecture Re: OPNs (Circa 2003)

If $N = {q^k}{n^2}$ is an odd perfect number given in Eulerian form, is $n$ a square?

On the natural density of almost perfect numbers

Looking for an appropriate reference(s) for two conjectures on odd perfect numbers

A conjecture regarding odd perfect numbers

Does this Theorem 2 from Dandapat et al. imply that $\gcd(\sigma(p^k),\sigma(a^2)) > 1$?

On odd perfect numbers $p^k m^2$ with special prime $p$ satisfying $m^2 - p^k = 2^r t$ - Part II

On the nearest-square function and the quantity $m^2 - p^k$ where $p^k m^2$ is an odd perfect number

On odd perfect numbers and a GCD - Part II

On odd perfect numbers $q^k n^2$ satisfying $n^2 - q^k = 2^r t$

Does $n \mid \sigma(n^2)$, if $q^k n^2$ is an odd perfect number?

If $p^k m^2$ is an odd perfect number with special prime $p$, then must $m^2 - p^k = s^2 - t^2$ hold for some $s$ and $t$?

If $n$ is a multiperfect number, then necessarily does one of its prime factors $p$ satisfy $p \parallel n$?

Is the asymptotic density of positive integers $n$ satisfying $\gcd(n, \sigma(n^2))=\gcd(n^2, \sigma(n^2))$ equal to zero?

On attempting a proof for $r > 1$, if $M = {2^r}{b^2}$ is an even almost perfect number which is not a power of two

On the conjectured nonexistence of even almost perfect numbers (other than powers of two) and odd perfect numbers [closed]

Reference Request - Sharp Estimates for a Logarithmic Sum

A question on a special type of function

What proportion of the positive integers satisfy $I(n) < \frac{2n}{n + 1} \leq I(n^2) < 2$?

What are the divisors of $2n^2 - \sigma_{1}(n^2)$ for composite $n$?

Reference request: Research done on whether the Euler prime can be the largest factor of an odd perfect number

On Descartes / spoof odd perfect numbers

Does there exist an integer that is both solitary and almost perfect?

What proportion of the positive integers satisfy $I(n^2) < (1 + \frac{1}{n})I(n)$, where $I(x)$ is the abundancy index of $x$?