# On integers with a special divisibility property

William D. Banks; Florian Luca

Archivum Mathematicum (2006)

- Volume: 042, Issue: 1, page 31-42
- ISSN: 0044-8753

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topBanks, William D., and Luca, Florian. "On integers with a special divisibility property." Archivum Mathematicum 042.1 (2006): 31-42. <http://eudml.org/doc/249814>.

@article{Banks2006,

abstract = {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.},

author = {Banks, William D., Luca, Florian},

journal = {Archivum Mathematicum},

keywords = {Euler function; Carmichael function; Euler function; Carmichael function},

language = {eng},

number = {1},

pages = {31-42},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {On integers with a special divisibility property},

url = {http://eudml.org/doc/249814},

volume = {042},

year = {2006},

}

TY - JOUR

AU - Banks, William D.

AU - Luca, Florian

TI - On integers with a special divisibility property

JO - Archivum Mathematicum

PY - 2006

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 042

IS - 1

SP - 31

EP - 42

AB - 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.

LA - eng

KW - Euler function; Carmichael function; Euler function; Carmichael function

UR - http://eudml.org/doc/249814

ER -

## References

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- 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) MR1555183
- Ivić A., The Riemann-Zeta Function, Theory and Applications, Dover Publications, Mineola, New York, 2003. Zbl1034.11046MR1994094
- Luca F., Pomerance C., On the number of divisors of the Euler function, Publ. Math. Debrecen, to appear. MR2288471
- Tenenbaum G., Introduction to Analytic and Probabilistic Number Theory, Cambridge University Press, 1995. (1995) Zbl0880.11001MR1342300

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