Notes on Divisibility of Catalan Numbers
Combinatorics
2025-02-10 v1 Number Theory
Abstract
We investigate the divisibility properties of \sigma(C_n), the sum-of-divisors function applied to Catalan numbers, in relation to other number-theoretic functions. We establish conditions under which C_n has prime factors of the form 6k-1, derive sufficient criteria for divisibility of \sigma(C_n), and explore asymptotic estimates for the growth of \sigma(C_n) using de Bruijn's theorem. These results provide new insights into the arithmetic structure of Catalan numbers.
Keywords
Cite
@article{arxiv.2502.04619,
title = {Notes on Divisibility of Catalan Numbers},
author = {Volkan Yildiz},
journal= {arXiv preprint arXiv:2502.04619},
year = {2025}
}
Comments
7 pages, 1 figure