2025/02/07 by Volkan Yildiz, Yildiz, Volkan
Mathematics · Physics and Astronomy · #05A10 #05A16 #11A41 #11A51 #11B65 #Advanced Mathematical Identities #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2502.04619
openalex publication_date 2025/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the divisibility properties of σ(Cn), the sum-of-divisors function applied to Catalan numbers, in relation to other number-theoretic functions. We establish conditions under which Cn has prime factors of the form 6k-1, derive sufficient criteria for divisibility of σ(Cn), and explore asymptotic estimates for the growth of σ(Cn) using de Bruijn's theorem. These results provide new insights into the arithmetic structure of Catalan numbers.