{"id":"https://openalex.org/W2057829068","doi":"https://doi.org/10.1007/s40590-014-0045-3","title":"Arithmetic properties of the sum of the first $$n$$ n values of the Euler function","display_name":"Arithmetic properties of the sum of the first $$n$$ n values of the Euler function","publication_year":2014,"publication_date":"2014-09-01","ids":{"openalex":"https://openalex.org/W2057829068","doi":"https://doi.org/10.1007/s40590-014-0045-3","mag":"2057829068"},"language":"en","primary_location":{"id":"doi:10.1007/s40590-014-0045-3","doi":"https://doi.org/10.1007/s40590-014-0045-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40590-014-0045-3","pdf_url":null,"source":{"id":"https://openalex.org/S194854559","display_name":"Bolet\u00edn de la Sociedad Matem\u00e1tica Mexicana","issn_l":"2296-4495","issn":["2296-4495","1405-213X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bolet\u00edn de la Sociedad Matem\u00e1tica Mexicana","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5103258382","display_name":"R. Balasubramanian","orcid":"https://orcid.org/0000-0002-8183-8379","observed_orcids":["https://orcid.org/0000-0002-8183-8379"]},"institutions":[{"id":"https://openalex.org/I4210157032","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05e9bn444","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210157032"]},{"id":"https://openalex.org/I59611059","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05078rg59","country_code":"IN","type":"facility","lineage":["https://openalex.org/I59611059"]}],"countries":["ES","IN"],"is_corresponding":false,"raw_author_name":"R. Balasubramanian","raw_affiliation_strings":["The Institute of Mathematical Sciences, Chennai, 600 113, India","The Institute of Mathematical Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Institute of Mathematical Sciences, Chennai, 600 113, India","institution_ids":["https://openalex.org/I59611059"]},{"raw_affiliation_string":"The Institute of Mathematical Sciences","institution_ids":["https://openalex.org/I4210157032","https://openalex.org/I59611059"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007752336","display_name":"Florian Luca","orcid":"https://orcid.org/0000-0003-1321-4422","observed_orcids":["https://orcid.org/0000-0003-1321-4422"]},"institutions":[{"id":"https://openalex.org/I192619145","display_name":"University of the Witwatersrand","ror":"https://ror.org/03rp50x72","country_code":"ZA","type":"education","lineage":["https://openalex.org/I192619145"]},{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["MX","ZA"],"is_corresponding":true,"raw_author_name":"Florian Luca","raw_affiliation_strings":["Mathematical Institute, UNAM Juriquilla, 76230, Santiago de Quer\u00e9taro, M\u00e9xico","School of Mathematics, University of the Witwatersrand, P. O. Box Wits 2050, Johannesburg, South Africa","Mathematical Institute, UNAM Juriquilla","University of the Witwatersrand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, UNAM Juriquilla, 76230, Santiago de Quer\u00e9taro, M\u00e9xico","institution_ids":["https://openalex.org/I8961855"]},{"raw_affiliation_string":"School of Mathematics, University of the Witwatersrand, P. O. Box Wits 2050, Johannesburg, South Africa","institution_ids":["https://openalex.org/I192619145"]},{"raw_affiliation_string":"Mathematical Institute, UNAM Juriquilla","institution_ids":["https://openalex.org/I8961855"]},{"raw_affiliation_string":"University of the Witwatersrand","institution_ids":["https://openalex.org/I192619145"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031219698","display_name":"Dimbinaina Ralaivaosaona","orcid":"https://orcid.org/0000-0002-6350-5538","observed_orcids":["https://orcid.org/0000-0002-6350-5538"]},"institutions":[{"id":"https://openalex.org/I26092322","display_name":"Stellenbosch University","ror":"https://ror.org/05bk57929","country_code":"ZA","type":"education","lineage":["https://openalex.org/I26092322"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Dimbinaina Ralaivaosaona","raw_affiliation_strings":["Department of Mathematical Sciences, Stellenbosch University, Private Bag X1, Matieland, 7602, South Africa","Stellenbosch University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Stellenbosch University, Private Bag X1, Matieland, 7602, South Africa","institution_ids":["https://openalex.org/I26092322"]},{"raw_affiliation_string":"Stellenbosch University","institution_ids":["https://openalex.org/I26092322"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5007752336"],"corresponding_institution_ids":["https://openalex.org/I192619145","https://openalex.org/I8961855"],"apc_list":{"value":3290,"currency":"USD","value_usd":3290},"apc_paid":null,"fwci":0.989,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.71350422,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"21","issue":"1","first_page":"9","last_page":"17"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9994999766349792,"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":0.9994999766349792,"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":0.00039999998989515007,"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"}},{"id":"https://openalex.org/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/euler-function","display_name":"Euler function","score":0.8659999966621399},{"id":"https://openalex.org/keywords/summatory-functions","display_name":"summatory functions","score":0.9570000171661377},{"id":"https://openalex.org/keywords/counting-functions","display_name":"counting functions","score":0.8240000009536743},{"id":"https://openalex.org/keywords/perfect-squares","display_name":"perfect squares","score":0.5929999947547913},{"id":"https://openalex.org/keywords/upper-bounds","display_name":"upper bounds","score":0.5249999761581421},{"id":"https://openalex.org/keywords/arithmetic-properties","display_name":"arithmetic properties","score":0.609000027179718}],"concepts":[{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.7507383823394775},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.7060548663139343},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6698886752128601},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5392950773239136},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4966924786567688},{"id":"https://openalex.org/C2986362107","wikidata":"https://www.wikidata.org/wiki/Q7387108","display_name":"S function","level":2,"score":0.441877156496048},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.43126580119132996},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3881162703037262},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35715293884277344},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2721311151981354},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2700232267379761},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1256398856639862},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08068954944610596},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40590-014-0045-3","doi":"https://doi.org/10.1007/s40590-014-0045-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40590-014-0045-3","pdf_url":null,"source":{"id":"https://openalex.org/S194854559","display_name":"Bolet\u00edn de la Sociedad Matem\u00e1tica Mexicana","issn_l":"2296-4495","issn":["2296-4495","1405-213X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bolet\u00edn de la Sociedad Matem\u00e1tica Mexicana","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1462137042","https://openalex.org/W1595058606","https://openalex.org/W2020364392","https://openalex.org/W2051892877","https://openalex.org/W2069930861","https://openalex.org/W2077911692","https://openalex.org/W2082522764","https://openalex.org/W2135577229","https://openalex.org/W2322355077","https://openalex.org/W2615633464","https://openalex.org/W2738965834"],"related_works":["https://openalex.org/W2556586059","https://openalex.org/W2087301257","https://openalex.org/W2077451027","https://openalex.org/W4289730690","https://openalex.org/W1486904724","https://openalex.org/W2598304585","https://openalex.org/W7095418056","https://openalex.org/W1979585494","https://openalex.org/W2334342025","https://openalex.org/W2082376010"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2016-06-24T00:00:00"}