{"id":"W2094810794","doi":"10.1017/s1446788708000347","title":"ON THE INDEX OF COMPOSITION OF THE EULER FUNCTION AND OF THE SUM OF DIVISORS FUNCTION","year":2009,"lang":"en","type":"article","venue":"Journal of the Australian Mathematical Society","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université Laval","funders":"","keywords":"Mathematics; Integer (computer science); Composition (language); Function (biology); Combinatorics; Order (exchange); Value (mathematics); Divisor function; Euler's formula; Index (typography); Mathematical analysis; Divisor (algebraic geometry); Statistics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.004077035,0.000519346,0.001344313,0.002513629,0.001468574,0.003043422,0.001310007,0.000702465,0.003778664],"category_scores_gemma":[0.02211065,0.0004747246,0.0005551044,0.0009172702,0.004417879,0.006367418,0.002275016,0.00172581,0.0004054957],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001956751,"about_ca_system_score_gemma":0.0008190587,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004733081,"about_ca_topic_score_gemma":0.0003166234,"domain_scores_codex":[0.9990191,0.0003160008,0.00004328279,0.0001761681,0.0002628743,0.0001825875],"domain_scores_gemma":[0.9834109,0.01089851,0.001929135,0.0008310413,0.001002148,0.001928239],"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":[0.001183051,0.0001057946,0.01924616,0.0002209428,0.00005256707,0.0006192704,0.001023935,0.02386074,0.0160837,0.9182238,0.002666483,0.01671356],"study_design_scores_gemma":[0.00008513646,0.0002091292,0.01718316,0.0001683766,0.00009921389,0.001673841,0.0005326438,0.2658442,0.01866049,0.6860822,0.009335215,0.0001263914],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9383634,0.0009328994,0.03811051,0.0008795432,0.0001280207,0.00002254498,0.0001782797,0.0002115352,0.02117331],"genre_scores_gemma":[0.9837999,0.0004548554,0.01187314,0.00006778149,0.0001897525,0.00005773056,0.0001913681,0.0001749207,0.003190562],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004077035,"threshold_uncertainty_score":0.02156168,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05489877915936383,"score_gpt":0.3181579209799208,"score_spread":0.263259141820557,"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."}}