Timeline for Does the equation $\sigma(\sigma(x^2))=2x\sigma(x)$ have any odd solutions?
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
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| S Sep 4, 2020 at 5:04 | history | bounty ended | CommunityBot | ||
| S Sep 4, 2020 at 5:04 | history | notice removed | CommunityBot | ||
| Aug 31, 2020 at 13:50 | comment | added | Max Alekseyev | There are no other solutions below $10^{10}$. | |
| Aug 31, 2020 at 1:34 | comment | added | Jose Arnaldo Bebita | Thank you for the update, @DieterKadelka! I will take it from here. =) | |
| Aug 30, 2020 at 18:31 | comment | added | Dieter Kadelka | I had to stop my calculations above $x = 8 \cdot 10^8$ (I used my computer otherwise). Until then there have be no new solutions. I doubt if you find any solutions with this technique. | |
| Aug 29, 2020 at 3:35 | comment | added | Jose Arnaldo Bebita | Just checking, @DieterKadelka: Did you find any additional solutions to the equation in the range ${10}^8 \leq x \leq {10}^9$, apart from $x_1$ and $x_2$? | |
| Aug 27, 2020 at 13:13 | comment | added | Dieter Kadelka | About 1-2 hours, I did not measure the time exactly. My system is linux with 3,6 GHz and gp/pari from the pari group. If you access to a development system I would install gp/pari. | |
| Aug 27, 2020 at 13:09 | comment | added | Jose Arnaldo Bebita | I appreciate your assistance, @DieterKadelka! If I may just ask, how much time did it take to test the range ${10}^7 \leq x \leq {10}^8$ on your computer? | |
| Aug 27, 2020 at 13:04 | comment | added | Dieter Kadelka | Even below $x = 10^8$ there is no additional solution. Now I'll try the range until $x = 10^9$. | |
| Aug 27, 2020 at 10:06 | comment | added | Dieter Kadelka | Just by brute force with applying gp directly: The only solutions until $x=10000000$ are $x_1$ and $x_2$. I'm now trying the range until $x=100000000$. | |
| Aug 27, 2020 at 9:50 | comment | added | Jose Arnaldo Bebita | May I know why this question was downvoted as well? Some form of feedback, hopefully constructive, would go a long way towards improving future questions/posts. As it is, I am totally clueless. | |
| Aug 27, 2020 at 8:43 | comment | added | Jose Arnaldo Bebita | @C.F.G: I have edited my question to add the specific motivation for my original problem. | |
| Aug 27, 2020 at 8:36 | history | edited | Jose Arnaldo Bebita | CC BY-SA 4.0 |
added context / motivation for the original question (i.e. odd perfect numbers)
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| Aug 27, 2020 at 7:55 | comment | added | Jose Arnaldo Bebita | @C.F.G: Yes, this problem does stem from considerations involving the odd perfect number conjecture. | |
| Aug 27, 2020 at 7:50 | comment | added | C.F.G | Just to know: Does this come from odd perfect number conjecture? | |
| S Aug 27, 2020 at 3:55 | history | bounty started | Jose Arnaldo Bebita | ||
| S Aug 27, 2020 at 3:55 | history | notice added | Jose Arnaldo Bebita | Draw attention | |
| Aug 25, 2020 at 3:52 | comment | added | Jose Arnaldo Bebita | Note that $\sigma(x^2)$ is deficient, if the equation $$\sigma(\sigma(x^2))=2x\sigma(x)$$ holds. | |
| Aug 25, 2020 at 3:10 | history | edited | Jose Arnaldo Bebita | CC BY-SA 4.0 |
changed $p$ to $\rho$ in the upper bound for $\frac{\sigma(x^2)}{x\sigma(x)}$
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| Aug 25, 2020 at 2:33 | history | asked | Jose Arnaldo Bebita | CC BY-SA 4.0 |