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References (22)
-
P. Erdős, G. Tenenbaum (1999)
Ensembles of multiples of finite sets. (French)Discrete Mathematics, 200
-
S. Uchiyama (1971)
On some products involving primes, 28
-
E. Canfield, P. Erdös, C. Pomerance (1983)
On a problem of Oppenheim concerning “factorisatio numerorum”Journal of Number Theory, 17
-
Paul Erdös, G. Tenenbaum (1999)
Ensembles de multiples de suites finiesDiscret. Math., 200
-
E. Wirsing (1961)
Das asymptotische Verhalten von Summen über multiplikative FunktionenMathematische Annalen, 143
-
(1917)
The normal number of prime factors of an integer, -
A. Gelʹfond, I. Linnik, A. Feinstein, L. Mordell (1967)
Elementary methods in analytic number theoryAmerican Mathematical Monthly, 74
-
de Bruijn (1951)
On the number of positive integers $\leq x$ and free of prime factors $>y$, 54
-
(1961)
German) Math. Ann -
R. Hall (1996)
Sets of Multiples -
K. Williams (1974)
Merten's theorem for arithmetic progressionsJournal of Number Theory, 6
-
G. Alexits (2004)
Some unconventional problems in number theory -
M. Nathanson (1996)
Additive Number Theory: Inverse Problems and the Geometry of Sumsets -
R. Hall (1971)
On the distribution of divisors of integers in residue classes (mod k)Journal of Number Theory, 3
-
R. Bretèche (2000)
Répartition Des Diviseurs Dans Les Progressions ArithmétiquesBulletin of the London Mathematical Society, 32
-
P. Erdos, Haifa (2004)
ON THE DISTRIBUTION OF DIVISORS OF INTEGERS IN THE RESIDUE CLASSES ( MOD d ) -
S. Uchiyama (1971)
Shorter Notes: On Some Products Involving Primes, 28
-
K. Thanigasalam (1968)
On additive number theoryActa Arithmetica, 13
-
E. Landau (1974)
Handbuch der Lehre von der Verteilung der PrimzahlenMonatshefte für Mathematik und Physik, 22
-
P. Erdös, R. Hall (1976)
Proof of a conjecture about the distribution of divisors of integers in residue classesMathematical Proceedings of the Cambridge Philosophical Society, 79
-
P. Elliott (1998)
SETS OF MULTIPLES (Cambridge Tracts in Mathematics 118)Bulletin of The London Mathematical Society, 30
-
R. Hall (1992)
On some conjectures of Erdős in Astérisque, IJournal of Number Theory, 42
- Publisher
- de Gruyter
- Copyright
- © de Gruyter 2008
- ISSN
- 0933-7741
- eISSN
- 1435-5337
- DOI
- 10.1515/FORUM.2008.045
- Publisher site
- See Article on Publisher Site
Abstract
Let a be an integer and q a prime number. In this paper we find an asymptotic formula for the number of positive integers n ≤ x with the property that no divisor d > 1 of n lies in the arithmetic progression a modulo q .
Journal
Forum Mathematicum – de Gruyter
Published: Nov 1, 2008