| Title:
|
On a sequence formed by iterating a divisor operator (English) |
| Author:
|
Djamel, Bellaouar |
| Author:
|
Abdelmadjid, Boudaoud |
| Author:
|
Özer, Özen |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
69 |
| Issue:
|
4 |
| Year:
|
2019 |
| Pages:
|
1177-1196 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\mathbb {N}$ be the set of positive integers and let $s\in \mathbb {N}$. We denote by $d^{s}$ the arithmetic function given by $ d^{s}( n) =( d( n) ) ^{s}$, where $d(n)$ is the number of positive divisors of $n$. Moreover, for every $\ell ,m\in \mathbb {N}$ we denote by $\delta ^{s,\ell ,m}( n) $ the sequence $$ \underbrace {d^{s}( d^{s}( \ldots d^{s}( d^{s}( n) +\ell ) +\ell \ldots ) +\ell ) }_{m\text {-times}} =\begin {cases} d^{s}( n) & \text {for} \ m=1,\\ d^{s}( d^{s}( n) +\ell ) &\text {for} \ m=2,\\ d^{s}(d^{s}( d^{s}(n) +\ell ) +\ell ) & \text {for} \ m=3, \\ \vdots & \end {cases} $$ We present classical and nonclassical notes on the sequence $ ( \delta ^{s,\ell ,m}( n)) _{m\geq 1}$, where $\ell $, $n$, $s$ are understood as parameters. (English) |
| Keyword:
|
divisor function |
| Keyword:
|
prime number |
| Keyword:
|
iterated sequence |
| Keyword:
|
internal set theory |
| MSC:
|
03H05 |
| MSC:
|
11A25 |
| MSC:
|
11A41 |
| idZBL:
|
07144884 |
| idMR:
|
MR4039629 |
| DOI:
|
10.21136/CMJ.2019.0133-18 |
| . |
| Date available:
|
2019-11-28T08:55:06Z |
| Last updated:
|
2022-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147923 |
| . |
| Reference:
|
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| Reference:
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