no. 3
Gaps between consecutive divisors of factorials
Annales de l'Institut Fourier, Tome 43 (1993) no. 3, pp. 569-583.

On étudie l’ensemble de tous les diviseurs de n! dans l’ordre croissant, et l’on obtient une borne supérieure pour les écarts entre deux diviseurs consécutifs. Nous obtenons une borne inférieure pour la différence entre les deux diviseurs les plus proches de n!.

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.

@article{AIF_1993__43_3_569_0,
     author = {Berend, Daniel and Harmse, J. E.},
     title = {Gaps between consecutive divisors of factorials},
     journal = {Annales de l'Institut Fourier},
     pages = {569--583},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {43},
     number = {3},
     year = {1993},
     doi = {10.5802/aif.1348},
     zbl = {0790.11007},
     mrnumber = {94k:11107},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1348/}
}
TY  - JOUR
AU  - Berend, Daniel
AU  - Harmse, J. E.
TI  - Gaps between consecutive divisors of factorials
JO  - Annales de l'Institut Fourier
PY  - 1993
SP  - 569
EP  - 583
VL  - 43
IS  - 3
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1348/
DO  - 10.5802/aif.1348
LA  - en
ID  - AIF_1993__43_3_569_0
ER  - 
%0 Journal Article
%A Berend, Daniel
%A Harmse, J. E.
%T Gaps between consecutive divisors of factorials
%J Annales de l'Institut Fourier
%D 1993
%P 569-583
%V 43
%N 3
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1348/
%R 10.5802/aif.1348
%G en
%F AIF_1993__43_3_569_0
Berend, Daniel; Harmse, J. E. Gaps between consecutive divisors of factorials. Annales de l'Institut Fourier, Tome 43 (1993) no. 3, pp. 569-583. doi : 10.5802/aif.1348. https://aif.centre-mersenne.org/articles/10.5802/aif.1348/

[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. | MR | Zbl

[2] P. Erdös, Some problems and results in number theory, Number Theory and Combinatorics, Japan 1984, World Scientific, Singapore, 1985, 65-87. | Zbl

[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. | Zbl

[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. | MR | Zbl

[5] P. Erdös, Personal communication.

[6] R R. Hall and G. Tenenbaum, Divisors, Cambridge University Press, Cambridge, 1988. | MR | Zbl

[7] M. Queffélec, Substitution Dynamical Systems - Spectral Analysis, Springer-Verlag Lecture Notes, 1294, Berlin, 1987. | MR | Zbl

[8] G. Tenenbaum, Sur un problème extrémal en arithmétique, Ann. Inst. Fourier, Grenoble, 37-2 (1987), 1-18. | EuDML | Numdam | MR | Zbl

[9] M.D. Vose, Integers with consecutive divisors in small ratio, J. of Number Theory, 19 (1984), 233-238. | MR | Zbl

[10] M.D. Vose, Limit theorems for divisor distributions, Proc. Amer. Math. Soc., 95 (1985), 505-511. | MR | Zbl

[11] M D. Vose, The distribution of divisors of N!, Acta Arith., 50 (1988), 203-209. | MR | Zbl

Cité par Sources :