| Autor: |
Mehdi Hassani, Mahmoud Marie |
| Jazyk: |
angličtina |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
Mathematics Interdisciplinary Research, Vol 6, Iss 3, Pp 235-242 (2021) |
| Druh dokumentu: |
article |
| ISSN: |
2476-4965 |
| DOI: |
10.22052/mir.2021.240348.1254 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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