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arXiv · 2112.15551

Which numbers are not the sum plus the product of three positive integers?

Brian Conrey·Neil Shah
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Abstract

We investigate the number $R_3(n)$ of representations of $n$ as the sum plus the product of three positive integers. On average, $R_3(n)$ is $\frac{1}{2}\log^2 n$. We give an upper bound for $R_3(n)$ and an upper bound for the number of $n \leq N$ such that $R_3(n) = 0$. We conjecture that $R_3(n)= 0$ infinitely often.

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Brian Conrey, Neil Shah. 2021-12-31. Which numbers are not the sum plus the product of three positive integers?. https://arxiv.org/abs/2112.15551

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