On a problem of Sierpiński
Yong-Gao Chen (2012)
Acta Arithmetica
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Yong-Gao Chen (2012)
Acta Arithmetica
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Alfred Czogała (2001)
Mathematica Slovaca
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Juraj Kostra (1989)
Czechoslovak Mathematical Journal
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Jerzy Browkin, Hui-Qin Cao (2014)
Colloquium Mathematicae
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We discuss some cancellation algorithms such that the first non-cancelled number is a prime number p or a number of some specific type. We investigate which numbers in the interval (p,2p) are non-cancelled.
Nyman, Bertil, Nicely, Thomas R. (2003)
Journal of Integer Sequences [electronic only]
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Jean-Marie De Koninck, Jason Pierre Sweeney (2001)
Colloquium Mathematicae
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The main objective of this paper is to analyze the unimodal character of the frequency function of the largest prime factor. To do that, let P(n) stand for the largest prime factor of n. Then define f(x,p): = #{n ≤ x | P(n) = p}. If f(x,p) is considered as a function of p, for 2 ≤ p ≤ x, the primes in the interval [2,x] belong to three intervals I₁(x) = [2,v(x)], I₂(x) = ]v(x),w(x)[ and I₃(x) = [w(x),x], with v(x) < w(x), such that f(x,p) increases for p ∈ I₁(x), reaches its maximum...
P. Gallagher (1974)
Acta Arithmetica
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Magdalena Jastrzebska, Adam Grabowski (2006)
Formalized Mathematics
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We formalized some basic properties of the Möbius function which is defined classically as [...] as e.g., its multiplicativity. To enable smooth reasoning about the sum of this number-theoretic function, we introduced an underlying many-sorted set indexed by the set of natural numbers. Its elements are just values of the Möbius function.The second part of the paper is devoted to the notion of the radical of number, i.e. the product of its all prime factors.The formalization (which is...
Yingchun Cai (2002)
Acta Arithmetica
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K. Ramachandra (1971)
Acta Arithmetica
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Florian Luca, Paul Pollack (2012)
Acta Arithmetica
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