{"id":"https://openalex.org/W1984622554","doi":"https://doi.org/10.1080/10586458.1996.10504580","title":"Iterating the Sum-of-Divisors Function","display_name":"Iterating the Sum-of-Divisors Function","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W1984622554","doi":"https://doi.org/10.1080/10586458.1996.10504580","mag":"1984622554"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.1996.10504580","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://projecteuclid.org/journals/experimental-mathematics/volume-5/issue-2/Iterating-the-sum-of-divisors-function/em/1047565640.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110149813","display_name":"Graeme L. Cohen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Graeme L. Cohen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108510836","display_name":"H. J. J. te Riele","orcid":null},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Herman J. J. te Riele","raw_affiliation_strings":["CWI, Department of Numerical Mathematics , Kruislaan 413, 1098 SJ Amsterdam, The Netherlands E-mail: herman.te.riele@cwLnl"],"affiliations":[{"raw_affiliation_string":"CWI, Department of Numerical Mathematics , Kruislaan 413, 1098 SJ Amsterdam, The Netherlands E-mail: herman.te.riele@cwLnl","institution_ids":["https://openalex.org/I1341640284"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.636,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":10,"citation_normalized_percentile":{"value":0.670196,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":78,"max":79},"biblio":{"volume":"5","issue":"2","first_page":"91","last_page":"100"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.998,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9949,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/perfect-number","display_name":"Perfect number","score":0.78298336},{"id":"https://openalex.org/keywords/perfect-power","display_name":"Perfect power","score":0.5736908},{"id":"https://openalex.org/keywords/divisor-function","display_name":"Divisor function","score":0.5069566},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.48300564}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9209591},{"id":"https://openalex.org/C103996166","wikidata":"https://www.wikidata.org/wiki/Q170043","display_name":"Perfect number","level":2,"score":0.78298336},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7124309},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.68171436},{"id":"https://openalex.org/C93446932","wikidata":"https://www.wikidata.org/wiki/Q1972803","display_name":"Perfect power","level":2,"score":0.5736908},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.531639},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5280897},{"id":"https://openalex.org/C67056277","wikidata":"https://www.wikidata.org/wiki/Q915474","display_name":"Divisor function","level":3,"score":0.5069566},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.48300564},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40805215},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.20609224},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08034575},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.1996.10504580","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://projecteuclid.org/euclid.em/1047565640","pdf_url":"https://projecteuclid.org/journals/experimental-mathematics/volume-5/issue-2/Iterating-the-sum-of-divisors-function/em/1047565640.pdf","source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/4920","pdf_url":"https://ir.cwi.nl/pub/4920/04920D.pdf","source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":["Royal Netherlands Academy of Arts and Sciences"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/10355","pdf_url":"https://ir.cwi.nl/pub/10355/10355D.pdf","source":{"id":"https://openalex.org/S4306400859","display_name":"CWI's Institutional Repository (Centrum Wiskunde & Informatica)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1341640284","host_organization_name":"Centrum Wiskunde & Informatica","host_organization_lineage":["https://openalex.org/I1341640284"],"host_organization_lineage_names":["Centrum Wiskunde & Informatica"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"http://projecteuclid.org/euclid.em/1047565640","pdf_url":"https://projecteuclid.org/journals/experimental-mathematics/volume-5/issue-2/Iterating-the-sum-of-divisors-function/em/1047565640.pdf","source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":8,"referenced_works":["https://openalex.org/W1538837824","https://openalex.org/W1555475515","https://openalex.org/W1984622554","https://openalex.org/W1999338692","https://openalex.org/W2077762204","https://openalex.org/W2179025976","https://openalex.org/W2561123148","https://openalex.org/W833142133"],"related_works":["https://openalex.org/W4298031119","https://openalex.org/W4297382422","https://openalex.org/W4293357286","https://openalex.org/W2953344862","https://openalex.org/W2946980293","https://openalex.org/W2598214688","https://openalex.org/W2369380662","https://openalex.org/W2332182540","https://openalex.org/W2318277428","https://openalex.org/W2242409108"],"abstract_inverted_index":{"Let":[0],"\u03c30(n)":[1],"=":[2,8,32],"n":[3,24,110,117],"and":[4,15,43,47,132],"\u03c3":[5,16,29,129],"m":[6,12,30,75,94,107,134,138],"(n)":[7,31],"\u03c3(\u03c3":[9],"m\u20131(n)),":[10],"where":[11],"\u2265":[13,76,95],"1":[14,115],"is":[17,25,111],"the":[18,103,125],"sum-of-divisors":[19],"function.":[20],"We":[21,34,68,120],"say":[22],"that":[23,109],"(m,":[26,82,89,112],"k)perfect":[27],"if":[28],"kn.":[33],"have":[35,58,101],"tabulated":[36],"all":[37,44],"(2,k)-perfect":[38],"numbers":[39,50],"up":[40,51],"to":[41,52],"109":[42],"(3,":[45],"k)-":[46],"(4,":[48],"k)-perfect":[49,83],"2":[53],"\u00b7":[54],"108.":[55],"These":[56],"tables":[57],"suggested":[59],"several":[60],"conjectures,":[61],"some":[62],"of":[63,106,128],"which":[64],"we":[65,100],"prove":[66],"here.":[67],"ask":[69],"in":[70],"particular:":[71],"For":[72],"any":[73],"fixed":[74],"1,":[77],"are":[78],"there":[79],"infinitely":[80],"many":[81],"numbers?":[84],"Is":[85],"every":[86],"positive":[87],"integer":[88],"k)-perfect,":[90,113],"for":[91,114],"sufficiently":[92],"large":[93],"I?":[96],"In":[97],"this":[98],"connection,":[99],"obtained":[102],"smallest":[104],"value":[105],"such":[108],"\u2264":[116,118],"1000.":[119],"also":[121],"address":[122],"questions":[123],"concerning":[124],"limiting":[126],"behaviour":[127],"m+1(n)/\u03c3":[130],"m(n)":[131],"(\u03c3":[133],"(n))l/m":[135],",":[136],"as":[137],"\u2192":[139],"\u221e.":[140]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W1984622554","counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2024-12-10T20:47:33.557718","created_date":"2016-06-24"}