Notes on Divisibility of Catalan Numbers
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909482423943168 |
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| author | Yildiz, Volkan |
| author_facet | Yildiz, Volkan |
| contents | We investigate the divisibility properties of σ(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 σ(C_n), and explore asymptotic estimates for the growth of σ(C_n) using de Bruijn's theorem. These results provide new insights into the arithmetic structure of Catalan numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04619 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Notes on Divisibility of Catalan Numbers Yildiz, Volkan Combinatorics Number Theory 11A51, 11A41, 11B65, 05A10, 05A16 We investigate the divisibility properties of σ(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 σ(C_n), and explore asymptotic estimates for the growth of σ(C_n) using de Bruijn's theorem. These results provide new insights into the arithmetic structure of Catalan numbers. |
| title | Notes on Divisibility of Catalan Numbers |
| topic | Combinatorics Number Theory 11A51, 11A41, 11B65, 05A10, 05A16 |
| url | https://arxiv.org/abs/2502.04619 |