Gaps between consecutive divisors of factorials

Daniel Berend; J. E. Harmse

Annales de l'institut Fourier (1993)

  • Volume: 43, Issue: 3, page 569-583
  • ISSN: 0373-0956

Abstract

top
The set of all divisors of n ! , ordered according to increasing magnitude, is considered, and an upper bound on the gaps between consecutive ones is obtained. We are especially interested in the divisors nearest n ! and obtain a lower bound on their distance.

How to cite

top

Berend, Daniel, and Harmse, J. E.. "Gaps between consecutive divisors of factorials." Annales de l'institut Fourier 43.3 (1993): 569-583. <http://eudml.org/doc/75012>.

@article{Berend1993,
abstract = {The set of all divisors of $n!$, ordered according to increasing magnitude, is considered, and an upper bound on the gaps between consecutive ones is obtained. We are especially interested in the divisors nearest $\sqrt\{n!\}$ and obtain a lower bound on their distance.},
author = {Berend, Daniel, Harmse, J. E.},
journal = {Annales de l'institut Fourier},
keywords = {consecutive divisors of factorials; gaps between divisors; divisor sequences; upper bounds; lower bounds},
language = {eng},
number = {3},
pages = {569-583},
publisher = {Association des Annales de l'Institut Fourier},
title = {Gaps between consecutive divisors of factorials},
url = {http://eudml.org/doc/75012},
volume = {43},
year = {1993},
}

TY - JOUR
AU - Berend, Daniel
AU - Harmse, J. E.
TI - Gaps between consecutive divisors of factorials
JO - Annales de l'institut Fourier
PY - 1993
PB - Association des Annales de l'Institut Fourier
VL - 43
IS - 3
SP - 569
EP - 583
AB - The set of all divisors of $n!$, ordered according to increasing magnitude, is considered, and an upper bound on the gaps between consecutive ones is obtained. We are especially interested in the divisors nearest $\sqrt{n!}$ and obtain a lower bound on their distance.
LA - eng
KW - consecutive divisors of factorials; gaps between divisors; divisor sequences; upper bounds; lower bounds
UR - http://eudml.org/doc/75012
ER -

References

top
  1. [1] D. BEREND and C.F. OSGOOD, On the equation P(x) = n! and a question of Erdös, J. of Number Theory, 42 (1992), 189-193. Zbl0762.11010MR93e:11016
  2. [2] P. ERDÖS, Some problems and results in number theory, Number Theory and Combinatorics, Japan 1984, World Scientific, Singapore, 1985, 65-87. Zbl0603.10001
  3. [3] P. ERDÖS, Some problems and results on additive and multiplicative number theory, Analytic Number Theory, (Philadelphia, 1980), Springer-Verlag Lecture Notes, 899 (1981), 171-182. Zbl0472.10002
  4. [4] P. ERDÖS, Some solved and unsolved problems of mine in number theory, Topics in Analytic Number Theory, University of Texas Press, Austin, 1985, 59-75. Zbl0596.10001MR804242
  5. [5] P. ERDÖS, Personal communication. 
  6. [6] R R. HALL and G. TENENBAUM, Divisors, Cambridge University Press, Cambridge, 1988. Zbl0653.10001MR90a:11107
  7. [7] M. QUEFFÉLEC, Substitution Dynamical Systems - Spectral Analysis, Springer-Verlag Lecture Notes, 1294, Berlin, 1987. Zbl0642.28013MR89g:54094
  8. [8] G. TENENBAUM, Sur un problème extrémal en arithmétique, Ann. Inst. Fourier, Grenoble, 37-2 (1987), 1-18. Zbl0622.10030MR88k:11004
  9. [9] M.D. VOSE, Integers with consecutive divisors in small ratio, J. of Number Theory, 19 (1984), 233-238. Zbl0543.10031MR86c:11003
  10. [10] M.D. VOSE, Limit theorems for divisor distributions, Proc. Amer. Math. Soc., 95 (1985), 505-511. Zbl0609.10041MR87i:11126
  11. [11] M D. VOSE, The distribution of divisors of N!, Acta Arith., 50 (1988), 203-209. Zbl0647.10038MR89j:11082

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.