@article {
author = {Hassani, Mehdi and Marie, Mahmoud},
title = {A Remark on the Factorization of Factorials},
journal = {Mathematics Interdisciplinary Research},
volume = {6},
number = {3},
pages = {235-242},
year = {2021},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2021.240348.1254},
abstract = {The subject of this paper is to study distribution of the prime factors p and their exponents, which we denote by vp (n!), in standard factorization of n! into primes. We show that for each θ > 0 the primes p not exceeding nθ eventually assume almost all value of the sum ∑p⩽nθ vp(n!). Also, we introduce the notion of θ-truncated factorial, defined by n!θ =∏p⩽nθ pvp (n!) and we show that the growth of log n!1/2 is almost half of growth of log n!1.},
keywords = {Factorial,Growth of arithmetic functions,Prime number},
url = {https://mir.kashanu.ac.ir/article_111895.html},
eprint = {https://mir.kashanu.ac.ir/article_111895_95cb4d730a26d08b2cc21d98d04876cb.pdf}
}