{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:5EZGQY4ADOZ3GSJW4NHQO7BHGS","short_pith_number":"pith:5EZGQY4A","schema_version":"1.0","canonical_sha256":"e9326863801bb3b34936e34f077c2734b2f4c7931422c9d507516163e8176988","source":{"kind":"arxiv","id":"1610.01063","version":3},"attestation_state":"computed","paper":{"title":"Quasiperfect numbers with the same exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tomohiro Yamada","submitted_at":"2016-10-04T16:09:35Z","abstract_excerpt":"We study some divisibility properties of quasiperfect numbers. We show that if $N=(p_1 p_2 \\cdots p_t)^{2a}=m^2$ is quasiperfect, then $2a+1$ is divisible by $3$ and $N$ has at least one prime factor smaller than $\\exp 716.7944$. Moreover, we find some lower bounds concerning quasiperfect numbers of the form $N=m^2$ with $m$ squarefree."},"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":"1610.01063","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-04T16:09:35Z","cross_cats_sorted":[],"title_canon_sha256":"c4c223d6935f877c69e548c9f39d7efc5e1d3203755fd492fc2384971458a039","abstract_canon_sha256":"4d388fa951caf9b2d74fa8490bcd85c44bd38fbe41c0b8a5eaacf52bc8b3bcb6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:21.192329Z","signature_b64":"uqPxwwEGKs3/iJKzd1LfRfj8EApLyatVRXH8MHoRA3de86k40ePDQErXSEILWLxP2Rpqk+Hk4vGBMBceXO7rCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9326863801bb3b34936e34f077c2734b2f4c7931422c9d507516163e8176988","last_reissued_at":"2026-05-18T00:29:21.191217Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:21.191217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasiperfect numbers with the same exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tomohiro Yamada","submitted_at":"2016-10-04T16:09:35Z","abstract_excerpt":"We study some divisibility properties of quasiperfect numbers. We show that if $N=(p_1 p_2 \\cdots p_t)^{2a}=m^2$ is quasiperfect, then $2a+1$ is divisible by $3$ and $N$ has at least one prime factor smaller than $\\exp 716.7944$. Moreover, we find some lower bounds concerning quasiperfect numbers of the form $N=m^2$ with $m$ squarefree."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01063","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.01063","created_at":"2026-05-18T00:29:21.191295+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.01063v3","created_at":"2026-05-18T00:29:21.191295+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01063","created_at":"2026-05-18T00:29:21.191295+00:00"},{"alias_kind":"pith_short_12","alias_value":"5EZGQY4ADOZ3","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"5EZGQY4ADOZ3GSJW","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"5EZGQY4A","created_at":"2026-05-18T12:30:01.593930+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5EZGQY4ADOZ3GSJW4NHQO7BHGS","json":"https://pith.science/pith/5EZGQY4ADOZ3GSJW4NHQO7BHGS.json","graph_json":"https://pith.science/api/pith-number/5EZGQY4ADOZ3GSJW4NHQO7BHGS/graph.json","events_json":"https://pith.science/api/pith-number/5EZGQY4ADOZ3GSJW4NHQO7BHGS/events.json","paper":"https://pith.science/paper/5EZGQY4A"},"agent_actions":{"view_html":"https://pith.science/pith/5EZGQY4ADOZ3GSJW4NHQO7BHGS","download_json":"https://pith.science/pith/5EZGQY4ADOZ3GSJW4NHQO7BHGS.json","view_paper":"https://pith.science/paper/5EZGQY4A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.01063&json=true","fetch_graph":"https://pith.science/api/pith-number/5EZGQY4ADOZ3GSJW4NHQO7BHGS/graph.json","fetch_events":"https://pith.science/api/pith-number/5EZGQY4ADOZ3GSJW4NHQO7BHGS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5EZGQY4ADOZ3GSJW4NHQO7BHGS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5EZGQY4ADOZ3GSJW4NHQO7BHGS/action/storage_attestation","attest_author":"https://pith.science/pith/5EZGQY4ADOZ3GSJW4NHQO7BHGS/action/author_attestation","sign_citation":"https://pith.science/pith/5EZGQY4ADOZ3GSJW4NHQO7BHGS/action/citation_signature","submit_replication":"https://pith.science/pith/5EZGQY4ADOZ3GSJW4NHQO7BHGS/action/replication_record"}},"created_at":"2026-05-18T00:29:21.191295+00:00","updated_at":"2026-05-18T00:29:21.191295+00:00"}