{"id":"https://openalex.org/W4296380573","doi":"https://doi.org/10.1080/00029890.2022.2115268","title":"Reciprocal Sums and Counting Functions","display_name":"Reciprocal Sums and Counting Functions","publication_year":2022,"publication_date":"2022-09-19","ids":{"openalex":"https://openalex.org/W4296380573","doi":"https://doi.org/10.1080/00029890.2022.2115268"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2022.2115268","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2022.2115268","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087838203","display_name":"Alex Rice","orcid":"https://orcid.org/0000-0002-2698-5122"},"institutions":[{"id":"https://openalex.org/I170532803","display_name":"Millsaps College","ror":"https://ror.org/0494reh34","country_code":"US","type":"education","lineage":["https://openalex.org/I170532803"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alex Rice","raw_affiliation_strings":["Department of Mathematics, Millsaps College, Jackson, MS 39210"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Millsaps College, Jackson, MS 39210","institution_ids":["https://openalex.org/I170532803"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5087838203"],"corresponding_institution_ids":["https://openalex.org/I170532803"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21897038,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"129","issue":"10","first_page":"903","last_page":"912"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.998199999332428,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reciprocal","display_name":"Reciprocal","score":0.8248611688613892},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6342883110046387},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34246736764907837},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3239020109176636},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.05631023645401001}],"concepts":[{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.8248611688613892},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6342883110046387},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34246736764907837},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3239020109176636},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.05631023645401001},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2022.2115268","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2022.2115268","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W567882188","https://openalex.org/W1022649828","https://openalex.org/W2009196521","https://openalex.org/W2023600080","https://openalex.org/W2079378932","https://openalex.org/W2097673562","https://openalex.org/W2108900323","https://openalex.org/W2335400162","https://openalex.org/W2397645375","https://openalex.org/W2963683228","https://openalex.org/W3038544589"],"related_works":["https://openalex.org/W2318653344","https://openalex.org/W1978042415","https://openalex.org/W3013626938","https://openalex.org/W2017331178","https://openalex.org/W2964072617","https://openalex.org/W2976797620","https://openalex.org/W2260035625","https://openalex.org/W235081597","https://openalex.org/W2179551630","https://openalex.org/W2335699373"],"abstract_inverted_index":{"Motivated":[0],"by":[1,21],"the":[2,6,33,38,48,54,57,67],"gentle":[3],"exploration":[4],"of":[5,8,12,40,56,66],"distribution":[7],"prime":[9],"numbers":[10],"typical":[11],"an":[13],"undergraduate":[14],"number":[15,39],"theory":[16],"course,":[17],"as":[18,20],"well":[19],"a":[22,44,61],"recent":[23],"breakthrough":[24],"result":[25],"in":[26],"arithmetic":[27],"combinatorics,":[28],"we":[29],"explore":[30],"connections":[31],"between":[32],"counting":[34],"function,":[35,51],"which":[36,52],"counts":[37],"elements":[41,58],"up":[42,59],"to":[43,60],"threshold":[45,62],"x,":[46,63],"and":[47],"reciprocal":[49],"sum":[50],"adds":[53],"reciprocals":[55],"for":[64],"subsets":[65],"natural":[68],"numbers.":[69]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}