On sums of three integers with a fixed number of prime factors
نویسندگان
چکیده
منابع مشابه
Approximating the number of integers free of large prime factors
Define Ψ(x, y) to be the number of positive integers n ≤ x such that n has no prime divisor larger than y. We present a simple algorithm that approximates Ψ(x, y) in O(y{ log log x log y + 1 log log y }) floating point operations. This algorithm is based directly on a theorem of Hildebrand and Tenenbaum. We also present data which indicate that this algorithm is more accurate in practice than o...
متن کاملOn Strings of Consecutive Integers with a Distinct Number of Prime Factors
Let ω(n) be the number of distinct prime factors of n. For any positive integer k let n = nk be the smallest positive integer such that ω(n + 1), . . . , ω(n + k) are mutually distinct. In this paper, we give upper and lower bounds for nk. We study the same quantity when ω(n) is replaced by Ω(n), the total number of prime factors of n counted with repetitions. Let ω(n) and Ω(n) denote respectiv...
متن کاملApproximating the number of integers without large prime factors
Ψ(x, y) denotes the number of positive integers ≤ x and free of prime factors > y. Hildebrand and Tenenbaum gave a smooth approximation formula for Ψ(x, y) in the range (log x)1+ < y ≤ x, where is a fixed positive number ≤ 1/2. In this paper, by modifying their approximation formula, we provide a fast algorithm to approximate Ψ(x, y). The computational complexity of this algorithm is O( √ (log ...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2005
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2005.04.013