Timeline for Asymptotic behavior of median of number of prime divisors
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 27, 2021 at 18:52 | comment | added | Fedor Petrov | @JosephVanName the result cited by Thomas works for both | |
| Oct 27, 2021 at 18:23 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
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| Oct 27, 2021 at 18:21 | comment | added | Dominic van der Zypen | That's right, Joseph, only distinct prime divisors, so $p(2^5) = 1$. Will edit the original question | |
| Oct 27, 2021 at 13:21 | comment | added | Joseph Van Name | Are you counting the number of distinct prime divisors? Is $p(2^{5})=1$? Is $p(2^{5})=5$? en.wikipedia.org/wiki/Prime_omega_function | |
| Oct 27, 2021 at 8:25 | comment | added | Thomas Bloom | The median is certainly unbounded, and grows like $\gg \log\log n$. This follows from the fact (Hardy-Ramanujan, reproved by Turan) that $p(a)=(1+o(1))\log\log a$ for almost all integers $a$. | |
| Oct 27, 2021 at 8:15 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
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| Oct 27, 2021 at 8:08 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |