The number of factorizations of numbers less than into factors less than

Author:
Douglas Hensley

Journal:
Trans. Amer. Math. Soc. **275** (1983), 477-496

MSC:
Primary 10H25; Secondary 10K20, 60F10

DOI:
https://doi.org/10.1090/S0002-9947-1983-0682714-6

MathSciNet review:
682714

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Abstract: Let be the number in the title. There is a function , concave and decreasing with and such that if then as with fixed,

**[1]**R. R. Bahadur,*Some limit theorems in statistics*, Chap. 2, SIAM, Philadelphia, Pa., 1971. MR**0315820 (47:4369)****[2]**N. G. deBruijn,*On the number of positive integers**and free of prime factors*. II, Nederl. Akad. Wetensch. Proc. Ser. A**69**(1966), 239-247. MR**0205945 (34:5770)****[3]**P. Erdös,*On some asymptotic formulas in the theory of "factirsatio numerorum"*, Ann. of Math. (2)**42**(1941), 989-993. Corrections to two of my papers, Ann. of Math. (2)**44**(1943), 647-651. MR**0005516 (3:165b)****[4]**A. Oppenheim,*On an arithmetic function*. II, J. London Math. Soc.**2**(1927), 123-130.**[5]**G. Szekeres and P. Turán,*Über das zweite Hauptproblem der "Factorisatio Numerorum"*, Acta Litt. Sci. Szeged**6**(1933), 143-154.**[6]**J. Vaaler,*The Berry-Esseen inequality and the central limit theorem*(to appear).**[7]**V. M. Zolotarev,*On the closeness of the distributions of two sums of independent random variables*, Theory Probab. Appl.**10**(1965), 472-479. MR**0189109 (32:6536)**

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DOI:
https://doi.org/10.1090/S0002-9947-1983-0682714-6

Article copyright:
© Copyright 1983
American Mathematical Society