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

Abstract

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In this note, we study those positive integers which are divisible by , where is the Carmichael function.

How to cite

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Banks, 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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  1. Bang A. S., Taltheoretiske Undersøgelser, Tidsskrift Mat. 4 (5) (1886), 70–80, 130–137. 
  2. De Koninck J. M., Luca F., Positive integers divisible by the sum of their prime factors, Mathematika, to appear. MR2261843
  3. Dickson L. E., A new extension of Dirichlet’s theorem on prime numbers, Messenger of Math. 33 (1904), 155–161. (1904) 
  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. (1923) MR1555183
  5. Ivić A., The Riemann-Zeta Function, Theory and Applications, Dover Publications, Mineola, New York, 2003. Zbl1034.11046MR1994094
  6. Luca F., Pomerance C., On the number of divisors of the Euler function, Publ. Math. Debrecen, to appear. MR2288471
  7. Tenenbaum G., Introduction to Analytic and Probabilistic Number Theory, Cambridge University Press, 1995. (1995) Zbl0880.11001MR1342300

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