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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 $3^k.$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1906.05027","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-06-12T09:33:30Z","cross_cats_sorted":[],"title_canon_sha256":"372f2caa8de955692d858641c1f981dbb8b09c51bb2d2df2929d9f46936aa775","abstract_canon_sha256":"9363e7ca14d5f62169b1238e087a03b20d04ed2bbae8a164da2299d16929ecfe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:29.721041Z","signature_b64":"h3RSAHHztnNXm2eE+XmLPFZAzfTs5HpdalGZM7cWnz/5VATPPAxYeAOl8/EM0hf+ApitZvyiORp2wH5Ylxg3BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59c73d1e5bc6a47b577be82f852c00cbcb33477f5167ddd3fee46a1855004985","last_reissued_at":"2026-05-17T23:43:29.720377Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:29.720377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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