{"id":"W2293861218","doi":"10.5539/jmr.v8n2p45","title":"An Extension of the Euler Phi-function to Sets of Integers Relatively Prime to 30","year":2016,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"History and Theory of Mathematics","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Multiplicative function; Combinatorics; Integer (computer science); Conjecture; Prime (order theory); Coprime integers; Prime factor; Extension (predicate logic); Prime number; Arithmetic function; Euler's totient function; Function (biology); Euler's formula; Discrete mathematics; 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":"codex-gemma-dda1882f352a","candidate_categories":["metaresearch"],"consensus_categories":[],"category_scores_codex":[0.010321,0.0001930094,0.0006564826,0.0005924633,0.0001471679,0.00001808045,0.0009502955,0.0001409137,0.0004108661],"category_scores_gemma":[0.01057647,0.000101528,0.0002453364,0.0005522469,0.0002776048,0.0002354868,0.0002141036,0.0004653353,0.00009452555],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002111937,"about_ca_system_score_gemma":0.0002334264,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002708997,"about_ca_topic_score_gemma":0.000005095336,"domain_scores_codex":[0.9955289,0.0006872405,0.001364557,0.0001901349,0.001876634,0.0003525347],"domain_scores_gemma":[0.9923657,0.003489814,0.0009436282,0.0009513714,0.001963692,0.0002857738],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"bench_or_experimental","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0007435385,0.003223922,0.000132044,0.001393141,0.0003346612,0.0000188097,0.03189786,0.00006520236,0.7160217,0.215276,0.02146881,0.009424396],"study_design_scores_gemma":[0.001207483,0.002835117,0.0005863955,0.005345088,0.0001444201,0.0001132839,0.004698694,0.0002625114,0.1155052,0.8661093,0.002884655,0.0003078332],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9108583,0.0000387594,0.08522176,0.0009118541,0.000292717,0.0006128929,0.00001176557,0.00001346507,0.002038483],"genre_scores_gemma":[0.9452542,0.00001430948,0.05319232,0.00002900292,0.00008948518,0.000007576745,1.128675e-7,0.00005551496,0.001357493],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6508332,"threshold_uncertainty_score":0.9977579,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1797011096025506,"score_gpt":0.4293295650167894,"score_spread":0.2496284554142388,"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."}}