{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/118327"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/118327","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Perfect numbers and other numbers defined by the sum of their divisors","abstract":"Perfect, abundant, and deficient numbers are defined in terms of the sum of the divisors function. The history and the discovery of perfect numbers is discussed, and the question of the existence of an odd perfect number is considered. There is a discussion of amicable pairs and multiply perfect numbers. Other numbers which are defined by the sum of their divisors are also introduced.","abstract_html":"Perfect, abundant, and deficient numbers are defined in terms of the sum of the divisors function. The history and the discovery of perfect numbers is discussed, and the question of the existence of an odd perfect number is considered. There is a discussion of amicable pairs and multiply perfect numbers. Other numbers which are defined by the sum of their divisors are also introduced.","abstract_has_math":false,"creators":["Hawkes, Kenneth Eugene"],"institution":"Virginia Polytechnic Institute and State University","degree_name":"M.S.","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1975,"date_issued":"1975","date_published":"1975","updated_at":"2026-07-24T05:56:30Z","subjects":[],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10919/118327","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Hawkes, Kenneth Eugene"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-03-12T20:23:14Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-03-12T20:23:14Z"]},{"key":"dc:date.issued","label":"Date","values":["1975"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Polytechnic Institute and State University"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10919/118327"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Perfect, abundant, and deficient numbers are defined in terms of the sum of the divisors function. The history and the discovery of perfect numbers is discussed, and the question of the existence of an odd perfect number is considered. There is a discussion of amicable pairs and multiply perfect numbers. Other numbers which are defined by the sum of their divisors are also introduced."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["M.S."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Perfect numbers and other numbers defined by the sum of their divisors"]}]}],"canonical_facts":{"dc:contributor.department":["Mathematics"],"dc:creator":["Hawkes, Kenneth Eugene"],"dc:date.accessioned":["2024-03-12T20:23:14Z"],"dc:date.available":["2024-03-12T20:23:14Z"],"dc:date.issued":["1975"],"dc:description.abstract":["Perfect, abundant, and deficient numbers are defined in terms of the sum of the divisors function. The history and the discovery of perfect numbers is discussed, and the question of the existence of an odd perfect number is considered. There is a discussion of amicable pairs and multiply perfect numbers. Other numbers which are defined by the sum of their divisors are also introduced."],"dc:description.degree":["M.S."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/10919/118327"],"dc:language.iso":["en"],"dc:publisher":["Virginia Polytechnic Institute and State University"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Perfect numbers and other numbers defined by the sum of their divisors"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["M.S."],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-24T05:56:30Z"}