Composite positive integers with an average prime factor

Florian Luca; Francesco Pappalardi

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A note on numbers with a large prime factor III

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Paul Erdös, Aleksandar Ivić (1982)

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Pocklington's Theorem and Bertrand's Postulate

Marco Riccardi (2006)

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The first four sections of this article include some auxiliary theorems related to number and finite sequence of numbers, in particular a primality test, the Pocklington's theorem (see [19]). The last section presents the formalization of Bertrand's postulate closely following the book [1], pp. 7-9.

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On the Properties of the Möbius Function

Magdalena Jastrzebska, Adam Grabowski (2006)

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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...