Timeline for Are the numbers $\varphi(n^2)\sigma(n^2)\ (n=1,2,3,\ldots)$ pairwise distinct?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 19, 2020 at 7:35 | comment | added | Carl-Fredrik Nyberg Brodda | So what is the significance of this particular conjecture? Or is it just a member of the infinite family of conjectures whether $\varphi(n^k)\sigma(n^k)$ are all pairwise distinct for $k \geq 1$? | |
| Nov 19, 2020 at 1:01 | comment | added | Zhi-Wei Sun | In 2015 I conjectured that any positive rational number can be written as $m/n$ with $\varphi(m)$ and $\sigma(n)$ both squares. If $\varphi(m)$ and $\sigma(n)$ are both squares, then so is the product $\varphi(n)\sigma(n)$. Via computation I saw that $\varphi(n)\sigma(n)\ (n=1,2,3,\ldots)$ are not pairwise distinct. | |
| Nov 19, 2020 at 0:19 | history | edited | Zhi-Wei Sun | CC BY-SA 4.0 |
added 47 characters in body
|
| Nov 19, 2020 at 0:00 | history | edited | Zhi-Wei Sun | CC BY-SA 4.0 |
edited body
|
| Nov 18, 2020 at 23:48 | history | edited | Zhi-Wei Sun | CC BY-SA 4.0 |
deleted 2 characters in body
|
| Nov 18, 2020 at 23:38 | history | edited | Zhi-Wei Sun | CC BY-SA 4.0 |
Expand the text
|
| Nov 18, 2020 at 15:33 | comment | added | Carl-Fredrik Nyberg Brodda | What context does this problem arise in? | |
| Nov 18, 2020 at 14:44 | history | asked | Zhi-Wei Sun | CC BY-SA 4.0 |