{"id":"W2620630814","doi":"10.55016/ojs/cdm.v14i1.62425","title":"Generating Special Arithmetic Functions by Lambert Series Factorizations","year":2019,"lang":"en","type":"article","venue":"Contributions to Discrete Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Factorization; Euler's formula; Series (stratigraphy); Partition (number theory); Lambert W function; Inverse; Arithmetic function; Generating function; Divergent series; Algebra over a field; Arithmetic; Pure mathematics; Combinatorics; Discrete mathematics; Algorithm; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001213512,0.0006674624,0.0006560667,0.002444868,0.001114387,0.002338478,0.0008749853,0.0008521902,0.007278844],"category_scores_gemma":[0.003624467,0.000327988,0.0009134501,0.0009324703,0.00295853,0.004804159,0.001356089,0.001764109,0.001467993],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001132246,"about_ca_system_score_gemma":0.0004798805,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005121661,"about_ca_topic_score_gemma":0.0005346399,"domain_scores_codex":[0.9993793,0.0001205579,0.00002728687,0.0001013758,0.0002622766,0.0001091553],"domain_scores_gemma":[0.9991974,0.0003240303,0.0001106679,0.0001335418,0.0001543882,0.00007997611],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000006790387,0.000006720769,0.00005097815,0.0000147571,0.000001533723,0.00004413092,0.0001227177,0.000542663,0.000542993,0.995037,0.0004220548,0.003207664],"study_design_scores_gemma":[0.000005909245,0.00001392738,0.0000786119,0.00001549938,0.00000359713,0.0001080768,0.00005253534,0.007293232,0.0009879494,0.9882342,0.003194858,0.00001163203],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.327105,0.002477086,0.4503851,0.002540538,0.0008977974,0.00009243785,0.0002286901,0.0007587443,0.2155148],"genre_scores_gemma":[0.9191419,0.001599804,0.04960477,0.00051734,0.0009023913,0.00008911644,0.0001395358,0.000218477,0.02778649],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007278844,"threshold_uncertainty_score":0.02435011,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01507964982958641,"score_gpt":0.3020657537032398,"score_spread":0.2869861038736534,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}