Timeline for Size of finite subset of $\mathbb{N}$ such that the sum of reciprocals is a given positive integer
Current License: CC BY-SA 4.0
17 events
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| May 27, 2019 at 17:28 | vote | accept | Dominic van der Zypen | ||
| May 27, 2019 at 16:50 | answer | added | Lucia | timeline score: 11 | |
| May 27, 2019 at 15:45 | comment | added | Gerhard Paseman | This is almost a duplicate of my question exact packing of the harmonic series. I conjecture (and probably am not the first to do so) that the answer is O(exp(k+1)). Further, I suspect a minimal set has all its members with denominators less than exp(k+1). Gerhard "Whose Line Is It Anyway?" Paseman, 2019.05.27. | |
| May 27, 2019 at 14:20 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
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| May 27, 2019 at 14:20 | comment | added | Dominic van der Zypen | Thanks @FedorPetrov I will change the question! | |
| May 27, 2019 at 12:45 | comment | added | Fedor Petrov | @DominicvanderZypen I suggest to change the question to "what is the asymptotic growth of $m(k)$" (even if the exponential lower bound is enough for you purpose, I think it is quite interesting in general to hold here). | |
| May 27, 2019 at 12:01 | comment | added | Gerry Myerson | Ernie Croot has some papers about Egyptian fractions that you might find worth a look. | |
| May 27, 2019 at 11:47 | comment | added | Gerald Edgar | ... but a comment there does mention the exponential lower bound. | |
| May 27, 2019 at 10:51 | comment | added | Gerald Edgar | The keyword for this is "Egyptian fractions". A related question is at math.se ... math.stackexchange.com/q/3185675/442 ... no "answer" is given there, either. | |
| May 27, 2019 at 10:38 | comment | added | Dominic van der Zypen | Thanks @FedorPetrov, can you post this as an answer so we can close this thread? | |
| May 27, 2019 at 10:16 | comment | added | Fedor Petrov | The sum of $N$ different Egyptian fractions (fractions with numerator 1 and positive integer denominator) is at most $\log N+O(1)$, that implies the exponential lower bound for $m(k)$. | |
| May 27, 2019 at 10:05 | review | Close votes | |||
| May 27, 2019 at 21:53 | |||||
| May 27, 2019 at 9:59 | comment | added | Dominic van der Zypen | Apologies to @GeraldEdgar, I changed the question (it also contained a typo). | |
| May 27, 2019 at 9:58 | comment | added | vidyarthi | I think this is somewhat related to harmonic numbers and the euler constant | |
| May 27, 2019 at 9:50 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
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| May 27, 2019 at 9:49 | comment | added | Gerald Edgar | You re asking in the wrong forum. | |
| May 27, 2019 at 9:47 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |