Jose Arnaldo Bebita Dris's user avatar
Jose Arnaldo Bebita Dris's user avatar
Jose Arnaldo Bebita Dris's user avatar
Jose Arnaldo Bebita Dris
  • Member for 13 years, 5 months
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16 votes
1 answer
2k views

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

14 votes
2 answers
1k views

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

9 votes
2 answers
737 views

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

6 votes
3 answers
4k views

Re: Mordell's Equation $y^2 = x^3 + k$ and Perfect Numbers

6 votes
0 answers
500 views

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

4 votes
1 answer
1k views

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

4 votes
1 answer
329 views

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

4 votes
1 answer
2k views

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

3 votes
2 answers
446 views

On the natural density of almost perfect numbers

3 votes
0 answers
172 views

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

3 votes
4 answers
1k views

A conjecture regarding odd perfect numbers

3 votes
0 answers
176 views

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

2 votes
2 answers
474 views

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

2 votes
2 answers
626 views

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

2 votes
0 answers
339 views

On odd perfect numbers and a GCD - Part II

2 votes
1 answer
336 views

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

2 votes
0 answers
723 views

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

2 votes
0 answers
111 views

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

2 votes
1 answer
166 views

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

2 votes
1 answer
253 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

2 votes
0 answers
203 views

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

2 votes
1 answer
649 views

Reference Request - Sharp Estimates for a Logarithmic Sum

2 votes
1 answer
329 views

A question on a special type of function

2 votes
1 answer
298 views

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

2 votes
0 answers
280 views

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

2 votes
1 answer
315 views

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

2 votes
0 answers
481 views

On Descartes / spoof odd perfect numbers

2 votes
1 answer
323 views

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

1 vote
2 answers
198 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 $x$?

1 vote
1 answer
441 views

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