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On the distribution of powerful numbers

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References

  1. P. T. Bateman andE. Grosswald, On a Theorem of Erdös and Szekeres.Illinois J. Math. 2 (1958), 88–98.

    MATH  MathSciNet  Google Scholar 

  2. P. Erdös andG. Szekeres, Über die Anzahl der Abelschen Gruppen gegebener Ordnung und über ein verwandtes zahlentheoretisches Problem.Acta sei. Math. Szeged VII, 11 (1934), 95–102.

    Google Scholar 

  3. M. N. Huxley andO. Trifonov, The Square-full numbers in an Interval.Proc. Cam. Philos. Soc. 119 (1996), 201–208.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Ivić andP. Shiu, The Distribution of Powerful Numbers.Illinois J. Math 26 (1982), 576–590.

    MATH  MathSciNet  Google Scholar 

  5. E. Krätzel, Divisor Problems and Powerful Numbers.Math. Nachr. 114 (1983), 97–104.

    Article  MATH  MathSciNet  Google Scholar 

  6. -,Lattice Points, Kluwer Academic Publishers 1988.

  7. —, Estimates in the General Divisor Problem.Abh. Math. Sem. Univ. Hamburg 62 (1992), 191–206.

    MATH  MathSciNet  Google Scholar 

  8. —, On the Distribution of Square-full and Cube-full Numbers.Mh. Math. 120 (1995), 105–119.

    Article  MATH  Google Scholar 

  9. H.-Q. Liu, The Number of Square-full Numbers in an Interval.Acta Arith. 64 (1993), 129–149.

    MATH  MathSciNet  Google Scholar 

  10. —, The Number of Cube-full Numbers in an Interval.Acta Arith. 67 (1994), 1–12.

    MATH  MathSciNet  Google Scholar 

  11. —, Divisor Problems of 4 and 3 Dimensions.Acta Arith. 73 (1995), 249–269.

    MATH  MathSciNet  Google Scholar 

  12. H. Menzer, The Distribution of Powerful Integers of Type 4.Mh. Math. 107, (1989) 69–75.

    Article  MATH  MathSciNet  Google Scholar 

  13. —,Exponentialsummen und verallgemeinerte Teilerprobleme. Habilitationsschrift, Jena 1992.

    MATH  Google Scholar 

  14. A. Mercier andW. G. Nowak, Problème des Diviseurs pour des Valeurs Polynômiales II.Ann. Sei. Math. Québec 16 (1992), 81–94.

    MATH  MathSciNet  Google Scholar 

  15. P. G. Schmidt, Zur Anzahl Abelscher Gruppen gegebener Ordnung II.Acta Arith. 13 (1968), 405–417.

    MATH  MathSciNet  Google Scholar 

  16. —, Über die Anzahl quadratvoller Zahlen in kurzen Intervallen und ein verwandtes Gitterpunktproblem.Corrigendum zu Acta Arith. 50 (1988), 195–201 (1988), ibid.54 (1990), 251-254.

    MATH  Google Scholar 

  17. R. Seibold,Die Verteilung der k-vollen und l-freien Zahlen. Dissertationsschrift, Jena 1995.

  18. M. Vogts, Many-dimensional Generalized Divisor Problems.Math. Nachr. 124 (1985), 103–121.

    Article  MATH  MathSciNet  Google Scholar 

  19. G. Yu, The Distribution of 4-full Numbers.Mh. Math. 118 (1994), 145–152.

    Article  MATH  Google Scholar 

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  1. Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität, D-07740, Jena, Germany

    H. Menzer

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  1. H. Menzer
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Menzer, H. On the distribution of powerful numbers. Abh.Math.Semin.Univ.Hambg. 67, 221–237 (1997). https://doi.org/10.1007/BF02940832

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