User Jose Arnaldo Bebita

1 vote

1 answer

446 views

Existence of Solutions to an Equation Involving the Sum-of-Divisors Function [Reference Request]

asked Mar 2, 2011 at 19:24

1 vote

0 answers

119 views

If $N = q^k n^2$ is an odd perfect number, and $n < q^{k+1}$, does it follow that $k > 1$?

asked Jun 29, 2016 at 18:47

1 vote

0 answers

256 views

On even almost perfect numbers other than powers of two

asked Apr 7, 2016 at 14:50

1 vote

1 answer

345 views

Is it possible to have an even superperfect number and an odd superperfect number whose product is an almost perfect number?

asked Apr 30, 2016 at 7:33

1 vote

1 answer

231 views

If $q^k n^2$ is an odd perfect number with Euler prime $q$, are the following statements known to hold in general? [closed]

asked May 25, 2015 at 10:39

1 vote

1 answer

235 views

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

asked Dec 18, 2015 at 14:30

1 vote

0 answers

452 views

Reference Request - Jakob Weisblat's "The Search for the Odd Perfect Number" [closed]

asked Feb 10, 2012 at 10:23

1 vote

0 answers

463 views

A question on (odd) perfect numbers

asked Apr 25, 2015 at 4:08

1 vote

0 answers

61 views

Is $N - \varphi(N)$ a square, if $N = q^k m^2$ is an odd perfect number with special prime $q$?

asked May 27 at 19:47

1 vote

1 answer

203 views

On the Diophantine equation $m^2 - p^k = 2^r t$, where $r \geq 2$ and $\gcd(2,t)=1$

asked Jun 24, 2021 at 10:44

1 vote

1 answer

321 views

On odd perfect numbers and a GCD - Part III

asked Sep 14, 2021 at 7:27

1 vote

2 answers

387 views

Improving the lower bound $I(n^2) > \frac{2(q-1)}{q}$ when $q^k n^2$ is an odd perfect number

asked Jan 24, 2021 at 13:27

1 vote

0 answers

141 views

Is there an integer $r \neq q$ (with $r>1$) such that $N = q^k n^2 = \frac{r(r+1)}{2}\cdot{d}$ is an odd perfect number with $d>1$?

asked Jan 25, 2017 at 8:32

1 vote

0 answers

167 views

On "Euclidean" odd perfect numbers

asked Apr 1, 2023 at 15:24

0 votes

1 answer

86 views

What can be said about $\gcd(N/q^{\alpha},\sigma(N/q^{\alpha}))$ where $N$ is an odd perfect number and $q^{\alpha} \parallel N$?

asked Nov 5, 2023 at 3:46

0 votes

1 answer

417 views

On a GCD approach to odd perfect numbers

asked Dec 10, 2023 at 5:44

0 votes

0 answers

55 views

If $p^k m^2$ is an odd perfect number with special prime $p$, is it possible to have $p = k$?

asked Feb 9 at 7:42

0 votes

1 answer

203 views

If $p^k m^2$ is an odd perfect number with special prime $p$, then under what other conditions on $\sigma(p^k)/2$ does $k=1$ follow?

asked Jul 26, 2022 at 7:22

0 votes

1 answer

114 views

Given that $H = \frac{n^2}{\sigma(q^k)/2} = G \times J^2$, where $q^k n^2$ is an odd perfect number, then what is the value of $\gcd(G, J)$?

asked Jan 8, 2023 at 2:04

0 votes

0 answers

107 views

On improving the upper bound $I(m^2) \leq \frac{2p}{p+1}$, if $p^k m^2$ is an odd perfect number with special prime $p$

asked Oct 13, 2021 at 4:26

0 votes

1 answer

101 views

Any results on $\gcd(N^2, D(N^2))$ where $N^2$ is deficient and $D(N^2)$ is the deficiency of $N^2$?

asked Oct 13, 2016 at 15:28

0 votes

1 answer

161 views

Proving $k = 1 \implies q = 5$, if $q^k n^2$ is an odd perfect number with Euler prime $q$

asked Dec 29, 2016 at 20:43

0 votes

2 answers

690 views

A simple question regarding the sum-of-divisors function

asked Mar 5, 2011 at 6:30

0 votes

1 answer

748 views

Question Re: Arian Berdellima's Papers On Odd Perfect Numbers [closed]

asked Jan 28, 2012 at 12:21

0 votes

1 answer

953 views

Perfect Numbers - On Mersenne and Euler Primes

asked Dec 10, 2010 at 18:17

0 votes

1 answer

314 views

Are all known $k$-multiperfect numbers (for $k > 2$) not squarefree?

asked Oct 5, 2013 at 23:12

-1 votes

1 answer

291 views

On odd perfect numbers $N$ given in the Eulerian form $N = {q^k}{n^2}$, Part II

asked Apr 8, 2015 at 20:19

-1 votes

1 answer

104 views

For $q$ prime and $\gcd(q, n) = 1$, can $N = qn^2$ be almost perfect?

asked Aug 13, 2014 at 7:59

-4 votes

2 answers

173 views

If $p^k m^2$ is an odd perfect number with special prime $p$, then $p^k < 2am$ for some positive integer $a < m$ [closed]

asked Apr 27 at 7:30

Stack Exchange Network

59 Questions

Existence of Solutions to an Equation Involving the Sum-of-Divisors Function [Reference Request]

If $N = q^k n^2$ is an odd perfect number, and $n < q^{k+1}$, does it follow that $k > 1$?

On even almost perfect numbers other than powers of two

Is it possible to have an even superperfect number and an odd superperfect number whose product is an almost perfect number?

If $q^k n^2$ is an odd perfect number with Euler prime $q$, are the following statements known to hold in general? [closed]

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

Reference Request - Jakob Weisblat's "The Search for the Odd Perfect Number" [closed]

A question on (odd) perfect numbers

Is $N - \varphi(N)$ a square, if $N = q^k m^2$ is an odd perfect number with special prime $q$?

On the Diophantine equation $m^2 - p^k = 2^r t$, where $r \geq 2$ and $\gcd(2,t)=1$

On odd perfect numbers and a GCD - Part III

Improving the lower bound $I(n^2) > \frac{2(q-1)}{q}$ when $q^k n^2$ is an odd perfect number

Is there an integer $r \neq q$ (with $r>1$) such that $N = q^k n^2 = \frac{r(r+1)}{2}\cdot{d}$ is an odd perfect number with $d>1$?

On "Euclidean" odd perfect numbers

What can be said about $\gcd(N/q^{\alpha},\sigma(N/q^{\alpha}))$ where $N$ is an odd perfect number and $q^{\alpha} \parallel N$?

On a GCD approach to odd perfect numbers

If $p^k m^2$ is an odd perfect number with special prime $p$, is it possible to have $p = k$?

If $p^k m^2$ is an odd perfect number with special prime $p$, then under what other conditions on $\sigma(p^k)/2$ does $k=1$ follow?

Given that $H = \frac{n^2}{\sigma(q^k)/2} = G \times J^2$, where $q^k n^2$ is an odd perfect number, then what is the value of $\gcd(G, J)$?

On improving the upper bound $I(m^2) \leq \frac{2p}{p+1}$, if $p^k m^2$ is an odd perfect number with special prime $p$

Any results on $\gcd(N^2, D(N^2))$ where $N^2$ is deficient and $D(N^2)$ is the deficiency of $N^2$?

Proving $k = 1 \implies q = 5$, if $q^k n^2$ is an odd perfect number with Euler prime $q$

A simple question regarding the sum-of-divisors function

Question Re: Arian Berdellima's Papers On Odd Perfect Numbers [closed]

Perfect Numbers - On Mersenne and Euler Primes

Are all known $k$-multiperfect numbers (for $k > 2$) not squarefree?

On odd perfect numbers $N$ given in the Eulerian form $N = {q^k}{n^2}$, Part II

For $q$ prime and $\gcd(q, n) = 1$, can $N = qn^2$ be almost perfect?

If $p^k m^2$ is an odd perfect number with special prime $p$, then $p^k < 2am$ for some positive integer $a < m$ [closed]