On the distribution of square-full and cube-full numbers |
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Authors: | Ekkehard Krätzel |
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Institution: | (1) Am Friedensberg 4, D-07745 Jena, Bundesrepublik Deutschland |
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Abstract: | There are many results on the distribution of square-full and cube-full numbers. In this article the distribution of these numbers are studied in more detail. Suchk-full numbers (k=2,3) are considered which are at the same time 1-free (1 k+2). At first an asymptotic result is given for the numberN
k,1(x) ofk-full and 1-free numbers not exceedingx. Then the distribution of these numbers in short intervals is investigated. We obtain different estimations of the differenceN
k,1(x+h)–Nk,1(x) in the casesk=2, 1=4,5,6,7,1 8 andk=3, 1=5,6,7, 1 8. |
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Keywords: | 11N25 |
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