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On the Number of Factorizations of an Integer
-
Ramachandran Balasubramanian
and
Florian Luca
Published/Copyright:
April 11, 2011
Abstract
Let ƒ(n) be the number of unordered factorizations of a positive integer n as a product of factors > 1. In this paper, we show that the number of distinct values of ƒ(n) below x is at most exp(9(log x2/3) for all x≥ 1.
Keywords.: Factorizations
Received: 2010-10-01
Accepted: 2010-12-20
Published Online: 2011-04-11
Published in Print: 2011-April
© de Gruyter 2011
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Keywords for this article
Factorizations
Articles in the same Issue
- Maximum GCD Among Pairs of Random Integers
- First Remark on a ζ-Analogue of the Stirling Numbers
- On Product Difference Fibonacci Identities
- New Sequences that Converge to a Generalization of Euler's Constant
- On the Number of Factorizations of an Integer
- Values of the Euler and Carmichael Functions which are Sums of Three Squares
- The Intrinsic Periodic Behaviour of Sequences Related to a Rational Integral
- Note on the Diophantine Equation Xt + Yt = BZt
- Coefficients in Powers of the Log Series
- On a Combinatorial Conjecture
- The (Exponential) Bipartitional Polynomials and Polynomial Sequences of Trinomial Type: Part I
- A Cauchy–Davenport Type Result for Arbitrary Regular Graphs
