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Displaying similar documents to “Sums of nonnegative multiplicative functions over integers without large prime factors II”

Normal numbers and the middle prime factor of an integer

Jean-Marie De Koninck, Imre Kátai (2014)

Colloquium Mathematicae

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Let pₘ(n) stand for the middle prime factor of the integer n ≥ 2. We first establish that the size of log pₘ(n) is close to √(log n) for almost all n. We then show how one can use the successive values of pₘ(n) to generate a normal number in any given base D ≥ 2. Finally, we study the behavior of exponential sums involving the middle prime factor function.

Prime Factorization of Sums and Differences of Two Like Powers

Rafał Ziobro (2016)

Formalized Mathematics

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Representation of a non zero integer as a signed product of primes is unique similarly to its representations in various types of positional notations [4], [3]. The study focuses on counting the prime factors of integers in the form of sums or differences of two equal powers (thus being represented by 1 and a series of zeroes in respective digital bases). Although the introduced theorems are not particularly important, they provide a couple of shortcuts useful for integer factorization,...