Timeline for How many divisors of $n$ are below $n^{1/3}$?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Feb 14, 2022 at 4:29 | vote | accept | Nico Tripeny | ||
| Aug 6, 2021 at 19:26 | answer | added | Will Sawin | timeline score: 11 | |
| Aug 6, 2021 at 19:06 | history | edited | Will Sawin | CC BY-SA 4.0 |
edited title
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| Aug 6, 2021 at 17:33 | history | edited | user44143 | CC BY-SA 4.0 |
retitled
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| Aug 6, 2021 at 17:30 | answer | added | FusRoDah | timeline score: 6 | |
| Aug 5, 2021 at 16:48 | history | edited | Nico Tripeny | CC BY-SA 4.0 |
Asked about a lower bound as well
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| Aug 5, 2021 at 14:41 | comment | added | Terry Tao | If one draws $d$ uniformly at random amongst the divisors of $n$, then $\log d$ is the sum of independent random variables (coming from each prime power in the factorisation of $n$), and $\sum_{d<n^{1/3}:d|n} 1 / \sum_{d|n} 1$ is the probability that this sum is less than $\frac{1}{3} \log n$. At this point one can apply one's favorite concentration of measure inequality (e.g., Bennett's inequality) to get an upper bound (the best bound to use depends on the regime of parameters such as $n$ or $\sum_{d|n} 1$ that you are most interested in). | |
| Aug 5, 2021 at 6:16 | review | Close votes | |||
| Aug 7, 2021 at 10:41 | |||||
| Aug 5, 2021 at 5:28 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
MathJax: \mid for divisibility
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| Aug 5, 2021 at 1:56 | review | First posts | |||
| Aug 5, 2021 at 6:00 | |||||
| Aug 5, 2021 at 1:54 | history | asked | Nico Tripeny | CC BY-SA 4.0 |