The distribution of 4-full numbers

 Access to full text

 Full (PDF)

1. [1] A. Baker, A Concise Introduction to the Theory of Numbers, Cambridge Univ. Press, 1984. Zbl0554.10001
2. [2] P. T. Bateman and E. Grosswald, On a theorem of Erdős and Szekeres, Illinois J. Math. 2 (1958), 88-98. Zbl0079.07104
3. [3] P. Erdős and G. Szekeres, Über die Anzahl der Abelschen Gruppen gegebener Ordnung und über ein verwandtes zahlentheoretisches Problem, Acta Sci. Math. (Szeged) 7 (1935), 95-102. Zbl60.0893.02
4. [4] A. Ivić, On the asymptotic formulas for powerful numbers, Publ. Inst. Math. (Belgrade) 23 (37) (1978), 85-94. Zbl0384.10025
5. [5] A. Ivić, On the number of finite non-isomorphic abelian groups in short intervals, Math. Nachr. 101 (1981), 257-271. Zbl0484.10028
6. [6] A. Ivić and P. Shiu, The distribution of powerful numbers, Illinois J. Math. 26 (1982), 576-590. Zbl0484.10024
7. [7] E. Krätzel, Zahlen k-ter Art, Amer. J. Math. 44 (1972), 309-328. Zbl0243.10037
8. [8] E. Krätzel, Divisor problems and powerful numbers, Math. Nachr. 114 (1983), 97-104. Zbl0545.10030
9. [9] E. Krätzel, Zweifache Exponentialsummen und dreidimensionale Gitterpunktprobleme, in: Elementary and Analytic Theory of Numbers, Banach Center Publ. 17, PWN, Warszawa, 1985, 337-369. 
10. [10] E. Krätzel, The distribution of powerful integers of type 4, Acta Arith. 52 (1989), 141-145. Zbl0646.10034
11. [11] H.-Q. Liu, On the number of abelian groups of a given order, Acta Arith. 59 (1991), 261-277. Zbl0737.11024
12. [12] H.-Q. Liu, On the number of abelian groups of a given order (supplement), Acta Arith. 64 (1993), 285-296. 
13. [13] H.-Q. Liu, The greatest prime factor of the integers in an interval, Acta Arith. 65 (1993), 301-328. Zbl0797.11071

1. Wenguang Zhai, Xiaodong Cao, On the average number of direct factors of finite abelian groups
2. Hong-Quan Liu, Divisor problems of 4 and 3 dimensions
3. Hong-Quan Liu, On some divisor problems
4. Wenguang Zhai, Xiaodong Cao, On the average number of unitary factors of finite abelian groups
5. Hong-Quan Liu, On a fundamental result in van der Corput's method of estimating exponential sums