7 дек. 2022 г. · For a positive integer n, the prime omega function value Ω(n):=∑p∣nνp(n) counts the number of prime divisors of n with multiplicities. A result ...

26 сент. 2023 г. · The prime omega function ω(n) counts the number of distinct prime factors of a natural number n, and can be defined as ω(n)=∑p∣n1. Let S(N)=∑Nn= ...

19 авг. 2022 г. · The value of ω(2n−1) is at least d(n)−2, where d(n) is the number of divisors of n. This follows from the Bang's theorem as the special case of ...

22 мая 2024 г. · If q is a prime, ϕ(q)=q−1. In general, ϕ is a multiplicative function, which counts how many integers in {1,2,…,q} are coprime to q. My answer ...

21 июн. 2020 г. · In particular, we know that Ω(n) is equally often even and odd. This statement is, in fact, equivalent to the prime number theorem.

10 дек. 2019 г. · Let ω(n) denote the number of distinct prime factors of a positive integer n. I was wondering what is known about the dirichlet series.

12 мар. 2019 г. · Upper bound for the integral over minor arcs of the exponential sum with prime omega function coefficients ... Define m as the union of the minor ...

21 апр. 2023 г. · Average value of the prime omega function Ω on predecessors of prime powers ... Estimates for Sum of Prime Factors and Number of Prime Factors.

25 июн. 2013 г. · Let's do some elementary math. olympiad style number theory. All we need to show is that for each fixed prime q, vq(pn−1)=o(n). Since gcd(pn−1,p ...

25 окт. 2016 г. · Let ω denote the number of distinct prime factors of a number n, and consider the minimal value w of this number as n ranges over the interval ( ...