EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.)
Vol. 76(90), pp. 89–99 (2004)

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THE DISTRIBUTION OFINTEGERS $n$ DIVISIBLE BY $l^{\omega(n)}$

F. Luca amd A. Sankaranarayanan

Instituto de Matematicas UNAM, Campus Morelia, Ap Postal 61-3 (Xangari) C.P. 58089 Morelia, Michoacan, Mexico and School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India

Abstract: Let $\omega(n)$ denote the number of distinct prime factors of the positive integer $n$. We study the cardinality of the set $\{n\le x:l^{\omega(n)}\mid n\}$, where $l\ge 2$ is any arbitrary positive integer which is sufficiently small with respect to $x$.

Classification (MSC2000): 11N25

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