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On the maximal order of numbers in the “factorisatio numerorum” problem

✍ Scribed by Martin Klazar; Florian Luca

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
208 KB
Volume
124
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let m(n) be the number of ordered factorizations of n 1 in factors larger than 1. We prove that for every ε > 0

holds for all integers n > n 0 , while, for a suitable constant c > 0,

holds for infinitely many positive integers n, where ρ = 1.72864 . . . is the positive real solution to ζ(ρ) = 2. We investigate also arithmetic properties of m(n) and the number of distinct values of m(n).

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