منابع مشابه
On Square-Free Numbers
In the article the formal characterization of square-free numbers is shown; in this manner the paper is the continuation of [19]. Essentially, we prepared some lemmas for convenient work with numbers (including the proof that the sequence of prime reciprocals diverges [1]) according to [18] which were absent in the Mizar Mathematical Library. Some of them were expressed in terms of clusters’ re...
متن کاملCounting Square-Free Numbers
The main topic of this contribution is the problem of counting square-free numbers not exceeding n. Before this work we were able to do it in time Õ( √ n). Here, the algorithm with time complexity Õ(n) and with memory complexity Õ(n) is presented. Additionally, a parallel version is shown, which achieves full scalability. As of now the highest computed value was for n = 10. Using our implementa...
متن کاملScheduling with Equipartition 2000
Note that an odd feature of this definition is that a sequential job completes work at a rate of even when absolutely no processors are allocated to it. This assumption makes things easier for the adversary and harder for any non-clairvoyant algorithm. Hence, it only makes these results stronger. A job phase with a nondecreasing speedup function executes no slower if it is allocated more pr...
متن کاملSome New Properties of Balancing Numbers and Square Triangular Numbers
A number N is a square if it can be written as N = n2 for some natural number n; it is a triangular number if it can be written as N = n(n + 1)/2 for some natural number n; and it is a balancing number if 8N2 +1 is a square. In this paper, we study some properties of balancing numbers and square triangular numbers.
متن کاملOn the Square Roots of Triangular Numbers
1. BALANCING NUMBERS We call an Integer n e Z a balancing number if 1+ 2+ --+ (»l ) = (w + l) + (w + 2) +••• + (» + >•) (1) for some r e Z. Here r is called the balancer corresponding to the balancing number n. For example, 6, 35, and 204 are balancing numbers with balancers 2, 14, and 84, respectively. It follows from (1) that, if n is a balancing number with balancer r, then n2^(n + r)(n + r ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1982
ISSN: 0012-365X
DOI: 10.1016/0012-365x(82)90226-6