On integers with a special divisibility property
Banks, William D. ; Luca, Florian
Archivum Mathematicum, Tome 042 (2006), p. 31-42 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 2006-01-01
Classification:  11N37
@article{107979,
     author = {William D. Banks and Florian Luca},
     title = {On integers with a special divisibility property},
     journal = {Archivum Mathematicum},
     volume = {042},
     year = {2006},
     pages = {31-42},
     zbl = {1164.11050},
     mrnumber = {2227110},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107979}
}
Banks, William D.; Luca, Florian. On integers with a special divisibility property. Archivum Mathematicum, Tome 042 (2006) pp. 31-42. http://gdmltest.u-ga.fr/item/107979/

Bang A. S. Taltheoretiske Undersøgelser, Tidsskrift Mat. 4 (5) (1886), 70–80, 130–137.

De Koninck J. M.; Luca F. Positive integers divisible by the sum of their prime factors, Mathematika, to appear. | MR 2261843

Dickson L. E. A new extension of Dirichlet’s theorem on prime numbers, Messenger of Math. 33 (1904), 155–161. (1904)

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. (1923) | MR 1555183

Ivić A. The Riemann-Zeta Function, Theory and Applications, Dover Publications, Mineola, New York, 2003. | MR 1994094 | Zbl 1034.11046

Luca F.; Pomerance C. On the number of divisors of the Euler function, Publ. Math. Debrecen, to appear. | MR 2288471

Tenenbaum G. Introduction to Analytic and Probabilistic Number Theory, Cambridge University Press, 1995. (1995) | MR 1342300 | Zbl 0880.11001