Which numbers are not the sum plus the product of three positive integers?
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2021
- DOI:
- 10.48550/arXiv.2112.15551
- arXiv:
- arXiv:2112.15551
- Bibcode:
- 2021arXiv211215551C
- Keywords:
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- Mathematics - Number Theory;
- 11D45;
- 11D72;
- 11D75;
- 11N36;
- 11N56