TY - JOUR
ID - 111895
TI - A Remark on the Factorization of Factorials
JO - Mathematics Interdisciplinary Research
JA - MIR
LA - en
SN - 2538-3639
AU - Hassani, Mehdi
AU - Marie, Mahmoud
AD - Department of Mathematics,
University of Zanjan,
University Blvd., 45371-38791
Zanjan, I. R. Iran
Y1 - 2021
PY - 2021
VL - 6
IS - 3
SP - 235
EP - 242
KW - Factorial
KW - Growth of arithmetic functions
KW - Prime number
DO - 10.22052/mir.2021.240348.1254
N2 - 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.
UR - https://mir.kashanu.ac.ir/article_111895.html
L1 - https://mir.kashanu.ac.ir/article_111895_95cb4d730a26d08b2cc21d98d04876cb.pdf
ER -