La résonance des multiples de 6 = 2*3 et d'un premier
Nous trouvons ici un extrait d'un bloc de la table R10000 triée par résonnance croissante (requête Resonance_Triee) où apparaissent en jaune les nombres de forme 6*P. Se mélangent à eux d'autres nombres dans l'ordre du tri des résonances, ayant d'autres décompositions notées d'une autre couleur. La colonne "Somme" correspond à la somme de toutes les périodes dans toutes les bases et la colonne "Carré de n-1" correspond au maximum théorique possible pour cette somme. Lorsqu'un diviseur commun existe pour ces deux valeurs, elles sont divisées d'autant (réduction de la fraction). On peut constater que les nombres de forme 6*P sont de moins en moins nombreux au fur et à mesure que la résonance croît.
Nombre
|
Décomposition
|
Somme
|
Carré de n-1
|
Résonance
|
9978
|
2x3x1663
|
58032069
|
99540529
|
0,715267622
|
9942
|
2x3x1657
|
57613911
|
98823481
|
0,715271178
|
9822
|
2x3x1637
|
56230971
|
96452041
|
0,71528322
|
9762
|
2x3x1627
|
55545801
|
95277121
|
0,715289352
|
9726
|
2x3x1621
|
11027343
|
18915125
|
0,715293067
|
9714
|
2x3x1619
|
55000689
|
94342369
|
0,715294312
|
9678
|
2x3x1613
|
54593619
|
93644329
|
0,715298064
|
9654
|
2x3x1609
|
54323079
|
93180409
|
0,715300582
|
9642
|
2x3x1607
|
54188061
|
92948881
|
0,715301845
|
9606
|
2x3x1601
|
10756803
|
18451205
|
0,715305654
|
9582
|
2x3x1597
|
53515491
|
91795561
|
0,715308209
|
9498
|
2x3x1583
|
52580949
|
90193009
|
0,715317253
|
9474
|
2x3x1579
|
52315449
|
89737729
|
0,715319867
|
9426
|
2x3x1571
|
10357293
|
17766125
|
0,715325134
|
9402
|
2x3x1567
|
51522981
|
88378801
|
0,715327787
|
9354
|
2x3x1559
|
50998029
|
87478609
|
0,715333136
|
9318
|
2x3x1553
|
50606079
|
86806489
|
0,715337183
|
9294
|
2x3x1549
|
50345619
|
86359849
|
0,715339899
|
9258
|
2x3x1543
|
49956189
|
85692049
|
0,715343999
|
9186
|
2x3x1531
|
9836373
|
16872845
|
0,715352295
|
9138
|
2x3x1523
|
48669009
|
83484769
|
0,715357898
|
9066
|
2x3x1511
|
9580953
|
16434845
|
0,715366415
|
8994
|
2x3x1499
|
47146569
|
80874049
|
0,715375068
|
8958
|
2x3x1493
|
46769739
|
80227849
|
0,715379447
|
8934
|
2x3x1489
|
46519359
|
79798489
|
0,715382385
|
8922
|
2x3x1487
|
46394421
|
79584241
|
0,71538386
|
8898
|
2x3x1483
|
1125489
|
1930649
|
0,715386823
|
8886
|
2x3x1481
|
9204123
|
15788645
|
0,71538831
|
8826
|
2x3x1471
|
9080193
|
15576125
|
0,715395807
|
3195
|
3^2x5x71
|
1486773
|
2550409
|
0,715399056
|
8754
|
2x3x1459
|
44662929
|
76615009
|
0,715404939
|
8718
|
2x3x1453
|
44296179
|
75986089
|
0,715409562
|
8706
|
2x3x1451
|
8834853
|
15155405
|
0,715411111
|
8682
|
2x3x1447
|
43930941
|
75359761
|
0,715414223
|
8634
|
2x3x1439
|
43446309
|
74528689
|
0,715420498
|
8598
|
2x3x1433
|
43084599
|
73908409
|
0,71542525
|
8574
|
2x3x1429
|
42844299
|
73496329
|
0,71542844
|
8562
|
2x3x1427
|
42724401
|
73290721
|
0,715430042
|
8538
|
2x3x1423
|
42485109
|
72880369
|
0,715433259
|
8454
|
2x3x1409
|
41652879
|
71453209
|
0,715444664
|
8394
|
2x3x1399
|
41063469
|
70442449
|
0,715452949
|
8286
|
2x3x1381
|
8002623
|
13728245
|
0,715468166
|
8238
|
2x3x1373
|
39550659
|
67848169
|
0,715475057
|
8202
|
2x3x1367
|
39205581
|
67256401
|
0,715480278
|
8166
|
2x3x1361
|
7772403
|
13333445
|
0,715485545
|
7962
|
2x3x1327
|
36943701
|
63377521
|
0,715516293
|
7926
|
2x3x1321
|
7322043
|
12561125
|
0,715521884
|
7914
|
2x3x1319
|
890229
|
1527209
|
0,715523758
|
7842
|
2x3x1307
|
35837961
|
61481281
|
0,715535128
|
7818
|
2x3x1303
|
35618829
|
61105489
|
0,715538964
|
7806
|
2x3x1301
|
7101903
|
12183605
|
0,715540891
|
7782
|
2x3x1297
|
35291391
|
60543961
|
0,715544763
|
7746
|
2x3x1291
|
6993093
|
11997005
|
0,715550615
|
7734
|
2x3x1289
|
34857159
|
59799289
|
0,715552578
|
7698
|
2x3x1283
|
34533249
|
59243809
|
0,715558504
|
7674
|
2x3x1279
|
34318149
|
58874929
|
0,715562486
|
7662
|
2x3x1277
|
34210851
|
58690921
|
0,715564486
|
7554
|
2x3x1259
|
33252729
|
57047809
|
0,715582772
|
7494
|
2x3x1249
|
32726319
|
56145049
|
0,715593159
|
4028
|
2^2x19x53
|
9452482
|
16216729
|
0,715605383
|
7422
|
2x3x1237
|
782931
|
1343201
|
0,715605845
|
7386
|
2x3x1231
|
6357873
|
10907645
|
0,715612281
|
7374
|
2x3x1229
|
31686099
|
54361129
|
0,71561444
|
7338
|
2x3x1223
|
31377309
|
53831569
|
0,71562096
|
7302
|
2x3x1217
|
31070031
|
53304601
|
0,715627545
|
7278
|
2x3x1213
|
30866019
|
52954729
|
0,715631971
|
7206
|
2x3x1201
|
6051603
|
10382405
|
0,715645425
|
7030
|
2x5x19x37
|
28797767
|
49406841
|
0,715648335
|
7158
|
2x3x1193
|
29856039
|
51222649
|
0,715654545
|
7122
|
2x3x1187
|
29556321
|
50708641
|
0,715661465
|
7086
|
2x3x1181
|
5851623
|
10039445
|
0,715668456
|
7026
|
2x3x1171
|
5752893
|
9870125
|
0,715680267
|
6978
|
2x3x1163
|
28372569
|
48678529
|
0,715689862
|
6918
|
2x3x1153
|
27886479
|
47844889
|
0,715702043
|
6906
|
2x3x1151
|
5557953
|
9535805
|
0,715704505
|
6774
|
2x3x1129
|
26736999
|
45873529
|
0,715732158
|
6738
|
2x3x1123
|
26453409
|
45387169
|
0,715739888
|
6702
|
2x3x1117
|
26171331
|
44903401
|
0,715747701
|
6654
|
2x3x1109
|
25797579
|
44262409
|
0,71575825
|
6618
|
2x3x1103
|
25519029
|
43784689
|
0,715766262
|
6582
|
2x3x1097
|
25241991
|
43309561
|
0,715774362
|
6558
|
2x3x1093
|
25058139
|
42994249
|
0,715779811
|
6546
|
2x3x1091
|
4993293
|
8567405
|
0,715782551
|
6522
|
2x3x1087
|
24783621
|
42523441
|
0,71578806
|
6414
|
2x3x1069
|
23969139
|
41126569
|
0,715813363
|
6378
|
2x3x1063
|
23700669
|
40666129
|
0,715821988
|
6366
|
2x3x1061
|
4722303
|
8102645
|
0,715824885
|
6306
|
2x3x1051
|
4633653
|
7950605
|
0,715839533
|
6294
|
2x3x1049
|
23080119
|
39601849
|
0,715842496
|
6234
|
2x3x1039
|
22641909
|
38850289
|
0,715857484
|
6198
|
2x3x1033
|
22380999
|
38402809
|
0,715866615
|
6186
|
2x3x1031
|
4458873
|
7650845
|
0,715869683
|
6126
|
2x3x1021
|
4372743
|
7503125
|
0,715885201
|
6114
|
2x3x1019
|
21778089
|
37368769
|
0,715888341
|
6078
|
2x3x1013
|
21522219
|
36929929
|
0,715897836
|
6054
|
2x3x1009
|
21352479
|
36638809
|
0,715904228
|
5982
|
2x3x997
|
20847291
|
35772361
|
0,715923714
|
5946
|
2x3x991
|
100473
|
172405
|
0,715933634
|
5898
|
2x3x983
|
20265549
|
34774609
|
0,715947049
|
5862
|
2x3x977
|
20018751
|
34351321
|
0,715957254
|
5826
|
2x3x971
|
3954693
|
6786125
|
0,715967586
|
5802
|
2x3x967
|
19610781
|
33651601
|
0,715974545
|
5718
|
2x3x953
|
19046679
|
32684089
|
0,715999361
|
7990
|
2x5x17x47
|
37193447
|
63824121
|
0,716004462
|
5682
|
2x3x947
|
18807441
|
32273761
|
0,716010222
|
5646
|
2x3x941
|
3713943
|
6373205
|
0,716021221
|
5622
|
2x3x937
|
18412071
|
31595641
|
0,716028631
|
5574
|
2x3x929
|
18098799
|
31058329
|
0,716043645
|
5514
|
2x3x919
|
17710989
|
30393169
|
0,716062779
|
5466
|
2x3x911
|
3480753
|
5973245
|
0,716078389
|
5442
|
2x3x907
|
17251161
|
29604481
|
0,716086297
|
5322
|
2x3x887
|
16498221
|
28313041
|
0,716126908
|
5298
|
2x3x883
|
16349649
|
28058209
|
0,716135252
|
5286
|
2x3x881
|
3255123
|
5586245
|
0,716139452
|
5262
|
2x3x877
|
16128051
|
27678121
|
0,716147909
|
5178
|
2x3x863
|
15616869
|
26801329
|
0,716178128
|
5154
|
2x3x859
|
15472329
|
26553409
|
0,716186943
|
5142
|
2x3x857
|
15400311
|
26429881
|
0,716191381
|
5118
|
2x3x853
|
15256779
|
26183689
|
0,71620032
|
5034
|
2x3x839
|
14759709
|
25331089
|
0,716232278
|
4974
|
2x3x829
|
14409699
|
24730729
|
0,716255766
|
4962
|
2x3x827
|
349761
|
600281
|
0,716260532
|
4938
|
2x3x823
|
14201709
|
24373969
|
0,716270133
|
4926
|
2x3x821
|
2826543
|
4851125
|
0,716274969
|
4866
|
2x3x811
|
2758053
|
4733645
|
0,716299505
|
4854
|
2x3x809
|
13722279
|
23551609
|
0,716304486
|
4782
|
2x3x797
|
13317891
|
22857961
|
0,716334891
|
4722
|
2x3x787
|
12985521
|
22287841
|
0,716360938
|
4638
|
2x3x773
|
12527259
|
21501769
|
0,716398535
|
4614
|
2x3x769
|
12397839
|
21279769
|
0,716409529
|
4566
|
2x3x761
|
2428203
|
4167845
|
0,716431863
|
4542
|
2x3x757
|
12013611
|
20620681
|
0,716443208
|
4506
|
2x3x751
|
2364753
|
4059005
|
0,716460451
|
4458
|
2x3x743
|
11572989
|
19864849
|
0,716483875
|
4434
|
2x3x739
|
11448609
|
19651489
|
0,716495777
|
4398
|
2x3x733
|
11263299
|
19333609
|
0,716513874
|
4362
|
2x3x727
|
11079501
|
19018321
|
0,71653227
|
4314
|
2x3x719
|
10836789
|
18601969
|
0,716557275
|
4254
|
2x3x709
|
10537179
|
18088009
|
0,716589326
|
4206
|
2x3x701
|
2060103
|
3536405
|
0,716615626
|
4146
|
2x3x691
|
2001693
|
3436205
|
0,716649356
|
4098
|
2x3x683
|
9777849
|
16785409
|
0,716677052
|
4062
|
2x3x677
|
9606651
|
16491721
|
0,716698254
|
4038
|
2x3x673
|
9493359
|
16297369
|
0,716712599
|
3966
|
2x3x661
|
1831503
|
3144245
|
0,716756675
|
3954
|
2x3x659
|
9102129
|
15626209
|
0,716764177
|
3918
|
2x3x653
|
8936979
|
15342889
|
0,716786959
|
3882
|
2x3x647
|
8773341
|
15062161
|
0,716810164
|
3015
|
3^2x5x67
|
1322829
|
2271049
|
0,716812226
|
3858
|
2x3x643
|
8665089
|
14876449
|
0,716825874
|
3846
|
2x3x641
|
1722243
|
2956805
|
0,716833803
|
4964
|
2^2x17x73
|
14346646
|
24631369
|
0,716872989
|
3786
|
2x3x631
|
1668873
|
2865245
|
0,716874202
|
7750
|
2x5^3x31
|
34974575
|
60047001
|
0,716875788
|
3714
|
2x3x619
|
8029689
|
13786369
|
0,716924404
|
3702
|
2x3x617
|
7977831
|
13697401
|
0,716932961
|
3678
|
2x3x613
|
7874619
|
13520329
|
0,716950242
|
3642
|
2x3x607
|
7721061
|
13256881
|
0,716976592
|
3606
|
2x3x601
|
1513803
|
2599205
|
0,717003467
|
3594
|
2x3x599
|
7518669
|
12909649
|
0,717012546
|
3558
|
2x3x593
|
7368639
|
12652249
|
0,717040148
|
3522
|
2x3x587
|
7220121
|
12397441
|
0,717068315
|
3462
|
2x3x577
|
6975951
|
11978521
|
0,717116562
|
3426
|
2x3x571
|
1366293
|
2346125
|
0,717146322
|
3414
|
2x3x569
|
6783639
|
11648569
|
0,717156382
|
8127
|
3^3x7x43
|
9613467
|
16507969
|
0,717171235
|
3378
|
2x3x563
|
6641169
|
11404129
|
0,717186989
|
3342
|
2x3x557
|
6500211
|
11162281
|
0,717218256
|
3282
|
2x3x547
|
6268641
|
10764961
|
0,717271894
|
9261
|
3^3x7^3
|
6241473
|
10718450
|
0,71729494
|
3246
|
2x3x541
|
1226343
|
2106005
|
0,717305028
|
3138
|
2x3x523
|
5730009
|
9840769
|
0,717408995
|
3126
|
2x3x521
|
1137243
|
1953125
|
0,717420991
|
3054
|
2x3x509
|
5426979
|
9320809
|
0,717494945
|
4828
|
2^2x17x71
|
13566002
|
23299929
|
0,71752363
|
3018
|
2x3x503
|
5299629
|
9102289
|
0,717533246
|
2994
|
2x3x499
|
127209
|
218489
|
0,717559292
|
2946
|
2x3x491
|
1009893
|
1734605
|
0,717612658
|
2922
|
2x3x487
|
4967421
|
8532241
|
0,717639999
|
2874
|
2x3x479
|
4805349
|
8254129
|
0,717696051
|
2802
|
2x3x467
|
4567281
|
7845601
|
0,717783732
|
2778
|
2x3x463
|
4489269
|
7711729
|
0,717813969
|
2766
|
2x3x461
|
890103
|
1529045
|
0,717829285
|
2742
|
2x3x457
|
4373511
|
7513081
|
0,717860319
|
2694
|
2x3x449
|
4221519
|
7252249
|
0,717924046
|
2658
|
2x3x443
|
4109289
|
7059649
|
0,717973353
|
2634
|
2x3x439
|
4035309
|
6932689
|
0,718006973
|
2598
|
2x3x433
|
3925599
|
6744409
|
0,718058569
|
2586
|
2x3x431
|
777873
|
1336445
|
0,718076087
|
2526
|
2x3x421
|
742143
|
1275125
|
0,718166176
|
2514
|
2x3x419
|
3675489
|
6315169
|
0,71818471
|
2454
|
2x3x409
|
3501879
|
6017209
|
0,7182801
|
2406
|
2x3x401
|
673203
|
1156805
|
0,718359841
|
2382
|
2x3x397
|
3299091
|
5669161
|
0,718400917
|
1690
|
2x5x13^2
|
1660061
|
2852721
|
0,718443479
|
2334
|
2x3x389
|
3167259
|
5442889
|
0,718485605
|
2298
|
2x3x383
|
3070149
|
5276209
|
0,718551445
|
2274
|
2x3x379
|
3006249
|
5166529
|
0,718596497
|
2238
|
2x3x373
|
2911659
|
5004169
|
0,718665888
|
2202
|
2x3x367
|
2818581
|
4844401
|
0,718737549
|
2154
|
2x3x359
|
2696829
|
4635409
|
0,718836827
|
2118
|
2x3x353
|
2607279
|
4481689
|
0,71891424
|
4556
|
2^2x17x67
|
12070234
|
20748025
|
0,718941406
|
2094
|
2x3x349
|
2548419
|
4380649
|
0,718967328
|
4485
|
3x5x13x23
|
1462071
|
2513282
|
0,718987655
|
2082
|
2x3x347
|
2519241
|
4330561
|
0,718994332
|
3003
|
3x7x11x13
|
1310631
|
2253001
|
0,719020075
|
7749
|
3^3x7x41
|
4365117
|
7503938
|
0,719069157
|
2022
|
2x3x337
|
2375871
|
4084441
|
0,719134162
|
1986
|
2x3x331
|
458373
|
788045
|
0,719222118
|
2745
|
3^2x5x61
|
273717
|
470596
|
0,719279402
|
7310
|
2x5x17x43
|
31071283
|
53421481
|
0,719320087
|
1902
|
2x3x317
|
2101731
|
3613801
|
0,719440309
|
1878
|
2x3x313
|
2048919
|
3523129
|
0,719506237
|
1866
|
2x3x311
|
404553
|
695645
|
0,719539838
|
1842
|
2x3x307
|
1970961
|
3389281
|
0,719608353
|
3572
|
2^2x19x47
|
7415518
|
12752041
|
0,719642647
|
1758
|
2x3x293
|
1794939
|
3087049
|
0,719862903
|
1698
|
2x3x283
|
1674249
|
2879809
|
0,720060158
|
1686
|
2x3x281
|
330123
|
567845
|
0,720101296
|
1662
|
2x3x277
|
1603851
|
2758921
|
0,720185354
|
2655
|
3^2x5x59
|
1023669
|
1760929
|
0,720213272
|
1626
|
2x3x271
|
306993
|
528125
|
0,720316098
|
1614
|
2x3x269
|
1512339
|
2601769
|
0,720360977
|
1578
|
2x3x263
|
1445469
|
2486929
|
0,720499713
|
7250
|
2x5^3x29
|
2776475
|
4777091
|
0,720559703
|
1542
|
2x3x257
|
1380111
|
2374681
|
0,720644934
|
1506
|
2x3x251
|
263253
|
453005
|
0,720797104
|
1446
|
2x3x241
|
242643
|
417605
|
0,721067577
|
1434
|
2x3x239
|
1193109
|
2053489
|
0,72112439
|
3458
|
2x7x13x19
|
6943321
|
11950849
|
0,721200705
|
6970
|
2x5x17x41
|
28216589
|
48566961
|
0,72122013
|
1398
|
2x3x233
|
1133799
|
1951609
|
0,721300689
|
1150
|
2x5^2x23
|
766955
|
1320201
|
0,721353926
|
4148
|
2^2x17x61
|
9990382
|
17197609
|
0,721416558
|
1374
|
2x3x229
|
1095099
|
1885129
|
0,72142336
|
1362
|
2x3x227
|
1076001
|
1852321
|
0,721486318
|
1338
|
2x3x223
|
1038309
|
1787569
|
0,721615627
|
1266
|
2x3x211
|
185853
|
320045
|
0,722033005
|
5115
|
3x5x11x31
|
3796503
|
6538249
|
0,722176698
|
4012
|
2^2x17x59
|
9340778
|
16088121
|
0,722353427
|
1194
|
2x3x199
|
826269
|
1423249
|
0,722500784
|
1182
|
2x3x197
|
809691
|
1394761
|
0,722584295
|
1158
|
2x3x193
|
777039
|
1338649
|
0,722756515
|
1146
|
2x3x191
|
152193
|
262205
|
0,722845335
|
3268
|
2^2x19x43
|
2064914
|
3557763
|
0,722959407
|
2852
|
2^2x23x31
|
4717318
|
8128201
|
0,723055558
|
1086
|
2x3x181
|
136623
|
235445
|
0,723318914
|
1074
|
2x3x179
|
668049
|
1151329
|
0,723419989
|
2385
|
3^2x5x53
|
206109
|
355216
|
0,723437599
|
6993
|
3^3x7x37
|
3545739
|
6111008
|
0,723479365
|
1038
|
2x3x173
|
623859
|
1075369
|
0,723737255
|
1002
|
2x3x167
|
581181
|
1002001
|
0,724077353
|
978
|
2x3x163
|
553569
|
954529
|
0,724318016
|
5890
|
2x5x19x31
|
20112089
|
34680321
|
0,724352005
|
942
|
2x3x157
|
513411
|
885481
|
0,724702042
|
3116
|
2^2x19x41
|
5625514
|
9703225
|
0,724860164
|
906
|
2x3x151
|
94953
|
163805
|
0,725116637
|
894
|
2x3x149
|
462219
|
797449
|
0,725262267
|
3604
|
2^2x17x53
|
7523006
|
12981609
|
0,725588016
|
6290
|
2x5x17x37
|
22919977
|
39551521
|
0,725635283
|
4785
|
3x5x11x29
|
127509
|
220064
|
0,725870331
|
834
|
2x3x139
|
402009
|
693889
|
0,726053397
|
110
|
2x5x11
|
6883
|
11881
|
0,726136859
|
822
|
2x3x137
|
390471
|
674041
|
0,726225507
|
4875
|
3x5^3x13
|
3440025
|
5938969
|
0,72643193
|
2668
|
2^2x23x29
|
4119242
|
7112889
|
0,726747057
|
786
|
2x3x131
|
71373
|
123245
|
0,72677343
|
762
|
2x3x127
|
335301
|
579121
|
0,72716753
|
2115
|
3^2x5x47
|
646749
|
1117249
|
0,727484697
|
3861
|
3^3x11x13
|
1077813
|
1862450
|
0,72798992
|
3542
|
2x7x11x23
|
7256191
|
12538681
|
0,727997651
|
5510
|
2x5x19x29
|
17562607
|
30349081
|
0,728051023
|
678
|
2x3x113
|
265119
|
458329
|
0,728767082
|
2812
|
2^2x19x37
|
1523126
|
2633907
|
0,729277158
|
654
|
2x3x109
|
246579
|
426409
|
0,729299738
|
642
|
2x3x107
|
237561
|
410881
|
0,729581034
|
3196
|
2^2x17x47
|
5901794
|
10208025
|
0,729647799
|
618
|
2x3x103
|
220029
|
380689
|
0,730176477
|
606
|
2x3x101
|
42303
|
73205
|
0,730491927
|
1935
|
3^2x5x43
|
540261
|
935089
|
0,730809738
|
582
|
2x3x97
|
194991
|
337561
|
0,731161951
|