Timeline for Estimating the sum $\sum_{1\leq x,y\leq n} \frac{x}{ \mathrm{lcm}(x,y)}$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 5, 2020 at 8:08 | vote | accept | kodlu | ||
| Apr 5, 2020 at 8:03 | history | edited | Alexey Ustinov | CC BY-SA 4.0 |
added 2146 characters in body
|
| Apr 5, 2020 at 3:15 | comment | added | kodlu | Great! Since I'm specifically interested in sum of $x/LCM(x,y)=GCD(x,y)/y,$ that case would be $\gamma=1,$ $\alpha=0,\beta=-1.$ When you have a chance, can you address that case please? | |
| Apr 5, 2020 at 1:43 | comment | added | Alexey Ustinov | @kodlu My answer will have another form if $\alpha=-1$ or $\beta=-1$ or $\alpha<-1$,... | |
| Apr 4, 2020 at 22:54 | comment | added | kodlu | Thanks. Your answer does not have a $\log n$ term, unlike Henri Cohen’s estimate, however, so the two seem inconsistent, if I let $LCM(x,y)=xy/(x,y)$. | |
| Apr 4, 2020 at 15:42 | history | answered | Alexey Ustinov | CC BY-SA 4.0 |