Timeline for Number of elements in the set $\{1,\cdots,n\}\cdot\{1,\cdots,n\}$
Current License: CC BY-SA 3.0
16 events
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Aug 14, 2015 at 19:04 | comment | added | Eric Naslund | @DavidZhang: It means that it is both $\ll$ and $\gg$. (The symbol $\sim$ means that the quotient tends to $1$) | |
| Aug 14, 2015 at 18:17 | comment | added | David Zhang | Excuse me, but what does $\asymp$ denote here? That the quotient of the two quantities tends to $1$ as $N \to \infty$? | |
| Aug 14, 2015 at 17:35 | history | edited | GH from MO | CC BY-SA 3.0 |
improved spelling
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| Aug 14, 2015 at 13:10 | comment | added | Eric Naslund | @FedorPetrov: Thank you for the correction - it is now fixed. | |
| Aug 14, 2015 at 13:10 | history | edited | Eric Naslund | CC BY-SA 3.0 |
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| S Jun 27, 2013 at 20:18 | history | suggested | Vít Tuček | CC BY-SA 3.0 |
fixed math formatting: \\{ ---> \lbrace
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| Jun 27, 2013 at 20:14 | review | Suggested edits | |||
| S Jun 27, 2013 at 20:18 | |||||
| Jun 25, 2013 at 8:03 | comment | added | Anthony Quas | @jernej: There's a very nice small book by Mark Kac about the number of prime factors of integers. Otherwise, try Hardy and Wright. | |
| Oct 7, 2012 at 8:27 | vote | accept | Kamalakshya | ||
| Oct 6, 2012 at 8:08 | comment | added | Jernej | @Kevin P. Costello Do you happen to know a book or survey paper covering these types of results as the one of Hardy and Ramanujan about almost all integers and their prime factors? | |
| Oct 6, 2012 at 4:48 | history | edited | Eric Naslund | CC BY-SA 3.0 |
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| Oct 6, 2012 at 4:44 | comment | added | Kevin P. Costello | If all you're looking to show is $o(n^2)$, then I believe Erdos' original argument can get you there somewhat faster. As a very rough sketch, the idea is: 1. By a result of Hardy and Ramnujan, almost all integers between $1$ and $n$ have roughly $\ln \ln (n^2)=\ln \ln n+O(1)$ prime factors. 2. Almost all pairs $(x,y)$ have approximately $2\ln \ln n$ prime factors dividing $xy$ (since $x$ and $y$ usually won't share many factors). 3. Since most products lie in only a small subset of $\{1,…,n^2\}$ (the numbers having an unusually large number of factors), most of the rest must remain uncovered. | |
| Oct 6, 2012 at 1:09 | history | edited | Eric Naslund | CC BY-SA 3.0 |
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| Oct 5, 2012 at 17:40 | comment | added | Felipe Voloch | Presumably $n=N$. | |
| Oct 5, 2012 at 17:29 | history | answered | Eric Naslund | CC BY-SA 3.0 |