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arXiv · 2011.11038

An identity involving number of representations of $n$ as a sum of $r$ triangular numbers

Sumit Kumar Jha
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Abstract

Let $\sum_{d|n}$ denote sum over divisors of a positive integer $n$, and $t_{r}(n)$ denote the number of representations of $n$ as a sum of $r$ triangular numbers. Then we prove that $$ \sum_{d|n}\frac{1+2\,(-1)^{d}}{d}=\sum_{r=1}^{n}\frac{(-1)^{r}}{r}\, \binom{n}{r}\, t_{r}(n) $$ using a result of Ono, Robbins and Wahl.

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Sumit Kumar Jha. 2020-11-18. An identity involving number of representations of $n$ as a sum of $r$ triangular numbers. https://arxiv.org/abs/2011.11038

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