Arithmetic properties of MacMahon-type sums of divisors
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910901251080192 |
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| author | Sellers, James A. Tauraso, Roberto |
| author_facet | Sellers, James A. Tauraso, Roberto |
| contents | In this paper, we prove several new infinite families of Ramanujan--like congruences satisfied by the coefficients of the generating function $U_t(a,q)$ which is an extension of MacMahon's generalized sum-of-divisors function. As a by-product, we also show that, for all $n\geq 0$, $\overline{B}_3(15n+7)\equiv 0 \pmod{5}$ where $\overline{B}_3(n)$ is the number of almost $3$-regular overpartitions of $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11404 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arithmetic properties of MacMahon-type sums of divisors Sellers, James A. Tauraso, Roberto Number Theory Combinatorics Primary 11P83, Secondary 11P81, 05A17 In this paper, we prove several new infinite families of Ramanujan--like congruences satisfied by the coefficients of the generating function $U_t(a,q)$ which is an extension of MacMahon's generalized sum-of-divisors function. As a by-product, we also show that, for all $n\geq 0$, $\overline{B}_3(15n+7)\equiv 0 \pmod{5}$ where $\overline{B}_3(n)$ is the number of almost $3$-regular overpartitions of $n$. |
| title | Arithmetic properties of MacMahon-type sums of divisors |
| topic | Number Theory Combinatorics Primary 11P83, Secondary 11P81, 05A17 |
| url | https://arxiv.org/abs/2411.11404 |