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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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*, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1971. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 4. MR**0315820****[2]**N. G. de Bruijn,*On the number of positive integers ≤𝑥 and free prime factors >𝑦. II*, Nederl. Akad. Wetensch. Proc. Ser. A 69=Indag. Math.**28**(1966), 239–247. MR**0205945****[3]**P. Erdös,*On some asymptotic formulas in the theory of the “factorisation numerorum.”*, Ann. of Math. (2)**42**(1941), 989–993. MR**0005516**, https://doi.org/10.2307/1968777**[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*, Teor. Verojatnost. i Primenen.**10**(1965), 519–526 (Russian, with English summary). MR**0189109**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
10H25,
10K20,
60F10

Retrieve articles in all journals with MSC: 10H25, 10K20, 60F10

Additional Information

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

Article copyright:
© Copyright 1983
American Mathematical Society