On the Number of Divisors of Binomial Coefficients
Matematičeskie zametki, Tome 93 (2013) no. 2, pp. 276-285
Voir la notice de l'article provenant de la source Math-Net.Ru
This paper deals with the problems of the upper and lower orders of growth of the ratios of the divisor functions of “adjacent” binomial coefficients, i.e., of the numbers of combinations of the form $C_{n}^{k}$ and $C_{n}^{k+1}$ or $C_{n}^{k}$ and $C_{n+1}^{k}$. The suprema and infima of the corresponding ratios are obtained.
Keywords:
number of divisors of binomial coefficients, sum of prime divisors.
G. V. Fedorov. On the Number of Divisors of Binomial Coefficients. Matematičeskie zametki, Tome 93 (2013) no. 2, pp. 276-285. http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a11/
@article{MZM_2013_93_2_a11,
author = {G. V. Fedorov},
title = {On the {Number} of {Divisors} of {Binomial} {Coefficients}},
journal = {Matemati\v{c}eskie zametki},
pages = {276--285},
year = {2013},
volume = {93},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a11/}
}
[1] P. Erdős, S. W. Graham, A. Ivić, C. Pomerance, “On the divisors of $n!$”, Analytic Number Theory, Vol. 1 (Allerton Park, IL, 1995), Progr. Math., 138, Birkhäuser Boston, Boston, MA, 1996, 337–355 | MR | Zbl
[2] S. Wigert, “Sur l'ordre de grandeur du nombre des diviseurs d'un entier”, Arkiv för Matematik, Astronomi och Fysik, 3 (1907), No 18 | Zbl
[3] S. Ramanujan, “Highly composite numbers”, Proc. London Math. Soc. (2), 14 (1915), 347–409 | Zbl
[4] A. A. Karatsuba, Osnovy analiticheskoi teorii chisel, Nauka, M., 1983 | MR | Zbl
[5] K. Prakhar, Raspredelenie prostykh chisel, Mir, M., 1967 | MR | Zbl