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arXiv · 2403.13533

On Sums of Practical Numbers and Polygonal Numbers

Sai Teja Somu·Duc Van Khanh Tran
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Abstract

Practical numbers are positive integers $n$ such that every positive integer less than or equal to $n$ can be written as a sum of distinct positive divisors of $n$. In this paper, we show that all positive integers can be written as a sum of a practical number and a triangular number, resolving a conjecture by Sun. We also show that all sufficiently large natural numbers can be written as a sum of a practical number and two $s$-gonal numbers.

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Sai Teja Somu, Duc Van Khanh Tran. 2024-03-20. On Sums of Practical Numbers and Polygonal Numbers. https://arxiv.org/abs/2403.13533

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