On the Number of Divisors of n!
by
Paul Erdős
,
S. W. Graham
,
Aleksandar Ivic
,
Carl Pomerance
BibTeX
@MISC{Erdős_onthe,
author = {Paul Erdős and S. W. Graham and Aleksandar Ivic and Carl Pomerance},
title = {On the Number of Divisors of n!},
year = {}
}
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
Several results involving d(n!) are obtained, where d(m) denotes the number of positive divisors of m. These include estimates for d(n!)/d((n - 1)!), d(n!) - d((n - 1)!), as well as the least number K with d((n +K)!)/d(n!) # 2.
Citations
| 108 | The Riemann zeta-function - Ivić - 1985 |
| 42 | der Corput’s method on exponential sums - Graham, Kolesnik, et al. - 1991 |
| 28 | Multiplicative Number Theory, 2nd ed - Davenport - 1980 |
| 27 | Applications of sieve methods to the theory of numbers - Hooley - 1976 |
| 19 | de Bruijn, “On the number of positive integers≤ x and free of prime factors > y - G - 1966 |
| 15 | On the normal density of primes in small intervals, and the difference between consecutive primes - Selberg - 1943 |
| 9 | A note on numbers with a large prime factor - Ramachandra - 1969 |
| 7 | On sums involving reciprocals of the largest prime factor of an integer - Ivić |
| 4 | On the prime factors - Erdős, Graham, et al. - 1975 |
| 1 | The greatest prime factor of the integers in a short interval - Chaohua - 1993 |
| 1 | The greatest prime factor of the integers in an interval - Liu - 1993 |
| 1 | un problème extrémal en arithmétique, Ann. Inst. Fourier 27 - Tenenbaum, Sur - 1987 |
