Timeline for Is any $n>60$ known to have a divisor sum greater than $e^{H_n}\log({H_n})$, where $H_n$ is the nth harmonic number?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 7, 2017 at 22:00 | vote | accept | CommunityBot | ||
| Aug 7, 2017 at 21:49 | answer | added | user41593 | timeline score: 7 | |
| Aug 7, 2017 at 21:26 | comment | added | user113088 | Many thanks. I've checked way past 5040, so the answer is no, and furthermore, there are no such $n$. Which is good, because it means the RH is true iff $\forall n\gt5040,\: \sigma(n)<e^{H_n}\log{H_n}$. If you write this into an answer, I will accept it. | |
| Aug 7, 2017 at 13:29 | review | Close votes | |||
| Aug 7, 2017 at 16:30 | |||||
| Aug 7, 2017 at 13:09 | comment | added | user41593 | Since $e^{H_n} \log H_n \geq e^\gamma n \log \log n$ for any $n \geq 3$, any counterexample to your inequality would violate Robin's inequality too, so if the Riemann hypothesis is true you shouldn't find any greater than $5040$. | |
| Aug 7, 2017 at 12:11 | review | First posts | |||
| Aug 7, 2017 at 12:12 | |||||
| Aug 7, 2017 at 12:08 | history | asked | user113088 | CC BY-SA 3.0 |