{"id":"https://openalex.org/W2077209879","doi":"https://doi.org/10.1090/s0025-5718-05-01798-9","title":"Approximating the number of integers without large prime factors","display_name":"Approximating the number of integers without large prime factors","publication_year":2005,"publication_date":"2005-12-02","ids":{"openalex":"https://openalex.org/W2077209879","doi":"https://doi.org/10.1090/s0025-5718-05-01798-9","mag":"2077209879"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-05-01798-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01798-9","pdf_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-05-01798-9/S0025-5718-05-01798-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-05-01798-9/S0025-5718-05-01798-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035143437","display_name":"Koji Suzuki","orcid":"https://orcid.org/0000-0002-3235-9558"},"institutions":[{"id":"https://openalex.org/I15009632","display_name":"Fuji Xerox (Japan)","ror":"https://ror.org/02w528w58","country_code":"JP","type":"company","lineage":["https://openalex.org/I15009632"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Koji Suzuki","raw_affiliation_strings":["Corporate Research Group, Fuji Xerox, 430, Sakai, Nakai-machi, Ashigarakami-gun, Kanagawa 259-0157, Japan"],"affiliations":[{"raw_affiliation_string":"Corporate Research Group, Fuji Xerox, 430, Sakai, Nakai-machi, Ashigarakami-gun, Kanagawa 259-0157, Japan","institution_ids":["https://openalex.org/I15009632"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5035143437"],"corresponding_institution_ids":["https://openalex.org/I15009632"],"apc_list":null,"apc_paid":null,"fwci":0.9142,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.81286469,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"75","issue":"254","first_page":"1015","last_page":"1024"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9969000220298767,"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"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9966999888420105,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.646998405456543},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.45090451836586},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.44807058572769165},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.41685137152671814},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38947421312332153},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3698703646659851},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.08003517985343933}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.646998405456543},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.45090451836586},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.44807058572769165},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.41685137152671814},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38947421312332153},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3698703646659851},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.08003517985343933},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-05-01798-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01798-9","pdf_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-05-01798-9/S0025-5718-05-01798-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.109.8052","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.109.8052","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2006-75-254/S0025-5718-05-01798-9/S0025-5718-05-01798-9.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.96.117","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.96.117","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2004-73-246/S0025-5718-03-01571-0/S0025-5718-03-01571-0.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-05-01798-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01798-9","pdf_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-05-01798-9/S0025-5718-05-01798-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2077209879.pdf","grobid_xml":"https://content.openalex.org/works/W2077209879.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W38104432","https://openalex.org/W74990011","https://openalex.org/W1511693980","https://openalex.org/W1994968438","https://openalex.org/W1997891615","https://openalex.org/W2013892149","https://openalex.org/W2053014383","https://openalex.org/W2073616076","https://openalex.org/W2082105013","https://openalex.org/W2086273850","https://openalex.org/W2088568314","https://openalex.org/W2088772065","https://openalex.org/W2090725688","https://openalex.org/W2106160186","https://openalex.org/W2123355614","https://openalex.org/W2128745083","https://openalex.org/W2159622301","https://openalex.org/W2323866234","https://openalex.org/W3009825533","https://openalex.org/W4206668612","https://openalex.org/W4229653025","https://openalex.org/W4235328030","https://openalex.org/W4243458565"],"related_works":["https://openalex.org/W2361861616","https://openalex.org/W2263699433","https://openalex.org/W2377979023","https://openalex.org/W2218034408","https://openalex.org/W2392921965","https://openalex.org/W2358755282","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2625833328"],"abstract_inverted_index":{"<inline-formula":[0,36,58,83,116,166,183,222,259,322],"content-type=\"math/mathml\">":[1,37,59,84,117,167,184,223,260,323],"<mml:math":[2,38,60,85,118,168,185,224,261,324],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[3,39,61,86,119,169,186,225,262,325],"alttext=\"normal":[4,87,226,326],"upper":[5,88,227,327],"Psi":[6,89,228,328],"left-parenthesis":[7,90,229,265,267,271,329],"x":[8,91,122,230,269,330],"comma":[9,92,231,331],"y":[10,93,130,159,232,273,332],"right-parenthesis\">":[11,94,233,276,333],"<mml:semantics>":[12,42,64,95,133,171,191,234,277,334],"<mml:mrow>":[13,43,65,96,134,192,235,278,335],"<mml:mi":[14,97,236,336],"mathvariant=\"normal\">\u03a8</mml:mi>":[15,98,237,337],"<mml:mo":[16,21,99,104,135,141,238,243,280,283,288,290,295,298,338,343],"stretchy=\"false\">(</mml:mo>":[17,100,136,239,281,284,291,339],"<mml:mi>x</mml:mi>":[18,45,101,139,153,240,287,340],"<mml:mo>,</mml:mo>":[19,102,241,341],"<mml:mi>y</mml:mi>":[20,67,103,151,242,294,342],"stretchy=\"false\">)</mml:mo>":[22,105,142,244,289,296,299,344],"</mml:mrow>":[23,46,68,106,148,154,198,200,245,300,345],"<mml:annotation":[24,47,69,107,155,173,201,246,301,346],"encoding=\"application/x-tex\">\\Psi":[25,108,247,347],"(x,y)</mml:annotation>":[26,109,248,348],"</mml:semantics>":[27,50,71,110,162,175,204,249,306,349],"</mml:math>":[28,51,72,111,163,176,205,250,307,350],"</inline-formula>":[29,52,112,177,351],"denotes":[30],"the":[31,114],"number":[32,182],"of":[33,55,255],"positive":[34,181],"integers":[35],"alttext=\"less-than-or-equal-to":[40,187],"x\">":[41,132],"<mml:mo>\u2264</mml:mo>":[44,152,193],"encoding=\"application/x-tex\">\\leq":[48,202],"x</mml:annotation>":[49,161],"and":[53,75,352],"free":[54],"prime":[56],"factors":[57],"alttext=\"greater-than":[62],"y\">":[63],"<mml:mo>&gt;</mml:mo>":[66,150],"encoding=\"application/x-tex\">&gt;y</mml:annotation>":[70],"</inline-formula>.":[73,206,251,308],"Hildebrand":[74],"Tenenbaum":[76],"gave":[77],"a":[78,179,217],"smooth":[79],"approximation":[80,213],"formula":[81],"for":[82,321],"in":[113],"range":[115],"alttext=\"left-parenthesis":[120],"log":[121,268,272],"right-parenthesis":[123,270,274],"Superscript":[124],"1":[125,188],"plus":[126],"epsilon":[127],"Baseline":[128],"greater-than":[129],"less-than-or-equal-to":[131],"<mml:mi>log</mml:mi>":[137,285,292],"<mml:mo>\u2061</mml:mo>":[138,286,293],"<mml:msup>":[140],"<mml:mrow":[143,195],"class=\"MJX-TeXAtom-ORD\">":[144,196],"<mml:mn>1</mml:mn>":[145,194],"<mml:mo>+</mml:mo>":[146],"<mml:mi>\u03f5</mml:mi>":[147,172],"</mml:msup>":[149],"encoding=\"application/x-tex\">(\\log":[156],"x)^{1+\\epsilon":[157],"}&gt;":[158],"\\leq":[160],"</inline-formula>,":[164],"where":[165],"alttext=\"epsilon\">":[170],"encoding=\"application/x-tex\">\\epsilon</mml:annotation>":[174],"is":[178,258,353],"fixed":[180],"slash":[189],"2\">":[190],"<mml:mo>/</mml:mo>":[197],"<mml:mn>2</mml:mn>":[199],"1/2</mml:annotation>":[203],"In":[207],"this":[208,256,316],"paper,":[209],"by":[210],"modifying":[211],"their":[212],"formula,":[214],"we":[215],"provide":[216],"fast":[218],"algorithm":[219,257,317],"to":[220],"approximate":[221],"The":[252],"computational":[253],"complexity":[254],"alttext=\"upper":[263],"O":[264],"StartRoot":[266],"EndRoot":[275],"<mml:mi>O</mml:mi>":[279],"<mml:msqrt>":[282],"</mml:msqrt>":[297],"encoding=\"application/x-tex\">O(\\sqrt":[302],"{(\\log":[303],"x)(\\log":[304],"y)})</mml:annotation>":[305],"We":[309],"give":[310],"numerical":[311],"results":[312],"which":[313],"show":[314],"that":[315],"provides":[318],"accurate":[319],"estimates":[320],"faster":[354],"than":[355],"conventional":[356],"methods":[357],"such":[358],"as":[359],"algorithms":[360],"exploiting":[361],"Dickman\u2019s":[362],"function.":[363]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
