| Autor: |
Feng, Lin, Li, Huixi, Wang, Biao |
| Zdroj: |
Indian Journal of Pure & Applied Mathematics; Dec2024, Vol. 55 Issue 4, p1440-1455, 16p |
| Abstrakt: |
In this paper, we mainly study the monomial-prime numbers, which are of the form p n k for primes p and integers k ≥ 2 . First, we give an asymptotic estimate on the number of numbers of a general form pf(n) for arithmetic functions f satisfying certain growth conditions, which generalizes Bhat's recent result on the Square-Prime Numbers. Then, we prove three Mertens-type theorems related to numbers of a more general form, partially extending the recent work of Qi-Hu, Popa and Tenenbaum on the Mertens sum evaluations. At the end, we evaluate the average and variance of the number of distinct monomial-prime factors of positive integers by applying our Mertens-type theorems. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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