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arXiv · 1609.08602

On the number of factorizations of an integer

R. Balasubramanian·Priyamvad Srivastav
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Abstract

Let $f(n)$ denote the number of unordered factorizations of a positive integer $n$ into factors larger than $1$. We show that the number of distinct values of $f(n)$, less than or equal to $x$, is at most $\exp \left( C \sqrt{\frac{\log x}{\log \log x}} \left( 1 + o(1) \right) \right)$, where $C=2\pi\sqrt{2/3}$ and $x$ is sufficiently large. This improves upon a previous result of the first author and F. Luca.

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R. Balasubramanian, Priyamvad Srivastav. 2016-09-27. On the number of factorizations of an integer. https://arxiv.org/abs/1609.08602

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