| Title:
|
On integers with a special divisibility property (English) |
| Author:
|
Banks, William D. |
| Author:
|
Luca, Florian |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
31-42 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note, we study those positive integers $n$ which are divisible by $\sum _{d|n}\lambda (d)$, where $\lambda (\cdot )$ is the Carmichael function. (English) |
| Keyword:
|
Euler function |
| Keyword:
|
Carmichael function |
| MSC:
|
11N37 |
| idZBL:
|
Zbl 1164.11050 |
| idMR:
|
MR2227110 |
| . |
| Date available:
|
2008-06-06T22:47:06Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107979 |
| . |
| Reference:
|
[1] Bang A. S.: Taltheoretiske Undersøgelser.Tidsskrift Mat. 4 (5) (1886), 70–80, 130–137. |
| Reference:
|
[2] De Koninck J. M., Luca F.: Positive integers divisible by the sum of their prime factors.Mathematika, to appear. MR 2261843 |
| Reference:
|
[3] Dickson L. E.: A new extension of Dirichlet’s theorem on prime numbers.Messenger of Math. 33 (1904), 155–161. |
| Reference:
|
[4] Hardy G. H., Littlewood J. E.: Some problems on partitio numerorum III. On the expression of a number as a sum of primes.Acta Math. 44 (1923), 1–70. MR 1555183 |
| Reference:
|
[5] Ivić A.: The Riemann-Zeta Function, Theory and Applications.Dover Publications, Mineola, New York, 2003. Zbl 1034.11046, MR 1994094 |
| Reference:
|
[6] Luca F., Pomerance C.: On the number of divisors of the Euler function.Publ. Math. Debrecen, to appear. MR 2288471 |
| Reference:
|
[7] Tenenbaum G.: Introduction to Analytic and Probabilistic Number Theory.Cambridge University Press, 1995. Zbl 0880.11001, MR 1342300 |
| . |
