Timeline for Is $\sum_{n=1}^\infty\frac{S(n)}{n!}$ an irrational, where $S(n)$ denotes the sum of remainders function?
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
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| S Nov 22, 2019 at 13:57 | history | bounty ended | user142929 | ||
| S Nov 22, 2019 at 13:57 | history | notice removed | user142929 | ||
| Nov 20, 2019 at 7:26 | vote | accept | user142929 | ||
| Nov 19, 2019 at 21:17 | answer | added | Fedor Petrov | timeline score: 6 | |
| Nov 19, 2019 at 20:32 | comment | added | user142929 | Many thanks for your generous and interesting comments, I don't know about it @SylvainJULIEN | |
| Nov 19, 2019 at 20:29 | comment | added | Sylvain JULIEN | Perhaps we could assume this number to be rational and figure out what its period may be. | |
| S Nov 19, 2019 at 20:14 | history | bounty started | user142929 | ||
| S Nov 19, 2019 at 20:14 | history | notice added | user142929 | Authoritative reference needed | |
| Sep 7, 2019 at 7:44 | answer | added | Thomas Browning | timeline score: 3 | |
| Sep 6, 2019 at 22:03 | answer | added | Ilya Bogdanov | timeline score: 7 | |
| Sep 6, 2019 at 21:41 | comment | added | user142929 | Many thanks @IlyaBogdanov feel free to add your reasoning as an answer, sure that it draw the attention of your colleagues. | |
| Sep 6, 2019 at 21:34 | comment | added | Ilya Bogdanov | This would follow from the fact that there are infinitely many $n$ with $n\mid S(n)$. Indeed, in this case the sum would have the form (integer)$/(n-1)!+$(something smallet than $1/(n-1)!$). The condition $n\mid S(n)$ may be relaxed further --- i.e., to $S(n)\mod n<n/(2+\varepsilon)$... | |
| Sep 1, 2019 at 19:37 | comment | added | Ali Taghavi | Thank you very much for your very kind words | |
| Sep 1, 2019 at 18:49 | comment | added | user142929 | I think that this MO site should appreciate and thank in some special way to professionals and serious mathematicians like you, and that are so generous as you offering your reputation in bounties. I would like to add my tribute dedicating you this post @AliTaghavi . Isn't required a response of this message, and good week. | |
| S Sep 1, 2019 at 18:39 | history | suggested | Ali Taghavi |
I add two tags.
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| Sep 1, 2019 at 18:36 | review | Suggested edits | |||
| S Sep 1, 2019 at 18:39 | |||||
| Sep 1, 2019 at 12:22 | comment | added | user142929 | Many thanks for your help @AlexeyUstinov | |
| Sep 1, 2019 at 11:12 | history | edited | Alexey Ustinov | CC BY-SA 4.0 |
deleted 16 characters in body
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| Sep 1, 2019 at 10:43 | comment | added | user142929 | See also, John B. Friedlander, Florian Luca and Mihai Stoiciu, On the irrationality of a divisor function series, INTEGERS: Electronic Journal of Combinatorial Number Theory 7, article #A31, (2007). | |
| Sep 1, 2019 at 10:43 | history | asked | user142929 | CC BY-SA 4.0 |