Timeline for Tuples of natural numbers with no mutual divisibility and large reciprocal sums
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 16 at 14:26 | comment | added | Peter Taylor | Am I understanding correctly that within each $E_i$ one element may divide another? If so, there may be interesting ideas where each $E_i$ is something like $\{m_i x : x \in X\}$ where $X$ is something like squarefree $k$-smooth numbers. | |
| Mar 15 at 21:29 | comment | added | Sophie M | You know, I tried that in the singleton case, and I don't think it helps there, at least when $C$ is not much larger than $(n \log n)^n$, but when $C$ can be bigger and the $|E_j|$'s can be bigger, too, it looks like it may help. I'll either revise or answer the question if I get anywhere with this. Thanks! | |
| Mar 15 at 20:52 | comment | added | Daniel Weber | It might be possible to consider all numbers of a form like $2^a 3^b 5^c$ with $a+b+c$ being some constant number. None of these divide each other, and there are quite a few, but their LCM is fairly small. | |
| Mar 15 at 20:12 | history | asked | Sophie M | CC BY-SA 4.0 |