%0 Journal Article
%T A Remark on the Factorization of Factorials
%J Mathematics Interdisciplinary Research
%I University of Kashan
%Z 2538-3639
%A Hassani, Mehdi
%A Marie, Mahmoud
%D 2021
%\ 09/01/2021
%V 6
%N 3
%P 235-242
%! A Remark on the Factorization of Factorials
%K Factorial
%K Growth of arithmetic functions
%K Prime number
%R 10.22052/mir.2021.240348.1254
%X 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.
%U https://mir.kashanu.ac.ir/article_111895_95cb4d730a26d08b2cc21d98d04876cb.pdf