Mehdi Hassani; Mahmoud Marie
Mathematics interdisciplinary research (Online),
09/2021, Letnik:
6, Številka:
3
Journal Article
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.
