{"paper":{"title":"Divisibility of Andrews' Singular Overpartitions by Powers of 2 and 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chiranjit Ray, Rupam Barman","submitted_at":"2019-06-12T09:33:30Z","abstract_excerpt":"Andrews introduced the partition function $\\overline{C}_{k, i}(n)$, called singular overpartition, which counts the number of overpartitions of $n$ in which no part is divisible by $k$ and only parts $\\equiv \\pm i\\pmod{k}$ may be overlined. He also proved that $\\overline{C}_{3, 1}(9n+3)$ and $\\overline{C}_{3, 1}(9n+6)$ are divisible by $3$ for $n\\geq 0$. Recently Aricheta proved that for an infinite family of $k$, $\\overline{C}_{3k, k}(n)$ is almost always even. In this paper, we prove that for any positive integer $k$, $\\overline{C}_{3, 1}(n)$ is almost always divisible by $2^k$ and $3^k.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05027","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}