Timeline for Are there infinitely many positive integers $\ n\ $ satisfying $\ \varphi(n)\mid \sigma(n)$?
Current License: CC BY-SA 4.0
6 events
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| Mar 26, 2022 at 6:14 | comment | added | Kapil | Note that both of these are multiplicative functions. Now $\varphi(p^k)=p^k(1-1/p)$ whereas $\sigma(p^k)=(p^k-1)/(p-1)$. If $p\geq 3$ and $k\geq 2$, then $\varphi(p^k)>\sigma(p^k)$. Hence, one might imagine that $n$ cannot be divisible by $p^2$ for $p\geq 3$. However, $n=270, 594, ...$ are in the sequence. In other words, the multiplicative properties alone are not enough to resolve this issue! | |
| Mar 26, 2022 at 3:01 | comment | added | markvs | @Aeryk: Did you look at these references? | |
| Mar 25, 2022 at 15:59 | history | edited | LSpice | CC BY-SA 4.0 |
Proofreading; `|` -> `\mid`
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| Mar 25, 2022 at 15:55 | comment | added | Aeryk | This is A020492 in the Online Encyclopedia of Integer Sequences. Most likely the references there will answer your question. oeis.org/A020492 | |
| S Mar 25, 2022 at 15:44 | review | First questions | |||
| Mar 25, 2022 at 15:47 | |||||
| S Mar 25, 2022 at 15:44 | history | asked | math110 | CC BY-SA 4.0 |