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2021
A positive integer p is called a prime, if p has exactly two different positive divisors. Every prime p is thus greater than 1 and it is divisible by itself and 1. Positive integers greater than 1 are called composite if they are not primes.
Michal Křížek +2 more
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A positive integer p is called a prime, if p has exactly two different positive divisors. Every prime p is thus greater than 1 and it is divisible by itself and 1. Positive integers greater than 1 are called composite if they are not primes.
Michal Křížek +2 more
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Journal of the London Mathematical Society, 1944
A (positive whole) number is called highly composite if it has more divisors than any smaller number, highly abundant if the sum of its divisors is greater than that for any smaller number, and superabundant if the sum of the reciprocals of its divisors is greater than that for any smaller number. The author uses \textit{A. E.
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A (positive whole) number is called highly composite if it has more divisors than any smaller number, highly abundant if the sum of its divisors is greater than that for any smaller number, and superabundant if the sum of the reciprocals of its divisors is greater than that for any smaller number. The author uses \textit{A. E.
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On Distinguishing Prime Numbers from Composite Numbers
The Annals of Mathematics, 1983zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Adleman, Leonard M. +2 more
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The least witness of a composite number
1998We consider the problem of finding the least witness of a composite number. If n is a composite number then a number w for which n is not a strong pseudo-prime to the base w is called a witness for n. Let w(n) be the least witness for a composite n. Bach [7] assuming the Generalized Riemann Hypothesis (GRH) showed that w(n) < 2log2 n.
R. Balasubramanian, S. V. Nagaraj
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On the Number and the Composition of Varieties
The Economic Journal, 2009At the same time, the composition of final goods may also differ across countries. Indeed, classical studies by Pyatt (1964) and Paroush (1965) examined priority patterns of final goods in Britain (using British Market Research Bureau Survey) and in Israel (using Labour Force Survey, Central Bureau of Statistics), respectively.
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Stick Numbers and Composition of Knots and Links
Journal of Knot Theory and Its Ramifications, 1997We address the concept of stick number for knots and links under various restrictions concerning the length of the sticks, the angles between sticks, and placements of the vertices. In particular, we focus on the effect of composition on the various stick numbers.
Adams, Colin C. +3 more
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The basis number of the composition of graphs
2012Summary: The basis number of a graph \(G\) is defined to be the least integer \(k\) such that \(G\) has a \(k\)-fold basis for its cycle space. We investigate the basis number of the composition of two paths, two cycles, a path and a cycle, a path and a wheel, a cycle and a wheel, a star and a wheel, a star and a path, a star and a cycle, a wheel and a
Hailat, Mohammad, Al-Zoubi, Ma'ared
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2012
In 1915, the London Mathematical Society published in its Proceedings a paper by Ramanujan entitled Highly Composite Numbers.
George E. Andrews, Bruce C. Berndt
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In 1915, the London Mathematical Society published in its Proceedings a paper by Ramanujan entitled Highly Composite Numbers.
George E. Andrews, Bruce C. Berndt
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Proceedings of the Institution of Electrical Engineers, 1963
A certain number system, governing combinatorial operations of elements of a given set, is provided. The operations are commutative, associative and distributive. The system rules countable sets of elements, i.e. parameters, such as define a complex number, and serves for precise and compact statements and for rational evaluation of explicit computable
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A certain number system, governing combinatorial operations of elements of a given set, is provided. The operations are commutative, associative and distributive. The system rules countable sets of elements, i.e. parameters, such as define a complex number, and serves for precise and compact statements and for rational evaluation of explicit computable
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Prime Numbers and Highly Composite Numbers
2012In 1915, Ramanujan wrote a long paper on “highly composite numbers.” This paper gives us a general method to analyse the growth of arithmetic functions. It is curious that this paper finds no discussion in Hardy’s “Twelve lectures.” In hindsight, we learn that the theory has a rich structure as well as interplay with other parts of number theory ...
M. Ram Murty, V. Kumar Murty
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