Timeline for A Lower Bound for the sum of the element orders in a cyclic group of order n
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 18, 2012 at 10:24 | comment | added | Andrea | I'm sorry, I was wrong. I meant to write $n = \sum_{d \vert} \phi(d)$. | |
| Jun 17, 2012 at 20:34 | comment | added | Yemon Choi | @Steven so by "the average of a sum" he means "the mean"? | |
| Jun 17, 2012 at 17:31 | comment | added | user9072 | @Patricia Hersh: I like that argument. | |
| Jun 17, 2012 at 16:13 | comment | added | Patricia Hersh | @quid: technically, one could use $\sum \phi (d) \le \sum d\phi (d)$, but obviously your answer is far better. | |
| Jun 17, 2012 at 12:54 | comment | added | Steven Gubkin | A sum' is a sum that remembers the number of summands. The average of a sum' is the sum divided by the number of summands. | |
| Jun 17, 2012 at 12:18 | comment | added | Yemon Choi | What in the name of Reilly is an average of a sum? | |
| Jun 17, 2012 at 11:45 | answer | added | user9072 | timeline score: 8 | |
| Jun 17, 2012 at 11:37 | comment | added | Patricia Hersh | @quid: good point. Is it easy to see that there is an infinite sequence of odd numbers $n_1 < n_2 < n_3 < \dots $ where this average keeps decreasing in value? For instance, the odd primes would not work. | |
| Jun 17, 2012 at 11:01 | comment | added | user9072 | @Patricia Hersh: Maybe, but then it does not seem to answer the question. | |
| Jun 17, 2012 at 10:57 | comment | added | Patricia Hersh | Maybe Andrea meant to write $n = \sum_{d|n} \phi (d)$? | |
| Jun 17, 2012 at 10:38 | comment | added | user9072 | I don't undertand the comment. I'd assume the phi is Euler totient but then the equality is false. | |
| Jun 17, 2012 at 10:02 | history | edited | Zhou ping | CC BY-SA 3.0 |
added 12 characters in body; added 3 characters in body
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| Jun 17, 2012 at 8:42 | comment | added | Andrea | I don't understand the question. $n = \sum_{d \vert n}\phi(d) d$. | |
| Jun 17, 2012 at 8:32 | history | asked | Zhou ping | CC BY-SA 3.0 |