A composite n such that 2n - 2 is divisible by n. more
The first 600 Poulet numbers :
341,
561,
645,
1105,
1387,
1729,
1905,
2047,
2465,
2701,
2821,
3277,
4033,
4369,
4371,
4681,
5461,
6601,
7957,
8321,
8481,
8911,
10261,
10585,
11305,
12801,
13741,
13747,
13981,
14491,
15709,
15841,
16705,
18705,
18721,
19951,
23001,
23377,
25761,
29341,
30121,
30889,
31417,
31609,
31621,
33153,
34945,
35333,
39865,
41041,
41665,
42799,
46657,
49141,
49981,
52633,
55245,
57421,
60701,
60787,
62745,
63973,
65077,
65281,
68101,
72885,
74665,
75361,
80581,
83333,
83665,
85489,
87249,
88357,
88561,
90751,
91001,
93961,
101101,
104653,
107185,
113201,
115921,
121465,
123251,
126217,
129889,
129921,
130561,
137149,
149281,
150851,
154101,
157641,
158369,
162193,
162401,
164737,
172081,
176149,
181901,
188057,
188461,
194221,
196021,
196093,
204001,
206601,
208465,
212421,
215265,
215749,
219781,
220729,
223345,
226801,
228241,
233017,
241001,
249841,
252601,
253241,
256999,
258511,
264773,
266305,
271951,
272251,
275887,
276013,
278545,
280601,
282133,
284581,
285541,
289941,
294271,
294409,
314821,
318361,
323713,
332949,
334153,
340561,
341497,
348161,
357761,
367081,
387731,
390937,
396271,
399001,
401401,
410041,
422659,
423793,
427233,
435671,
443719,
448921,
449065,
451905,
452051,
458989,
464185,
476971,
481573,
486737,
488881,
489997,
493697,
493885,
512461,
513629,
514447,
526593,
530881,
534061,
552721,
556169,
563473,
574561,
574861,
580337,
582289,
587861,
588745,
604117,
611701,
617093,
622909,
625921,
635401,
642001,
647089,
653333,
656601,
657901,
658801,
665281,
665333,
665401,
670033,
672487,
679729,
680627,
683761,
688213,
710533,
711361,
721801,
722201,
722261,
729061,
738541,
741751,
742813,
743665,
745889,
748657,
757945,
769567,
769757,
786961,
800605,
818201,
825265,
831405,
838201,
838861,
841681,
847261,
852481,
852841,
873181,
875161,
877099,
898705,
915981,
916327,
934021,
950797,
976873,
983401,
997633,
1004653,
1016801,
1018921,
1023121,
1024651,
1033669,
1050985,
1052503,
1052929,
1053761,
1064053,
1073021,
1082401,
1082809,
1092547,
1093417,
1104349,
1106785,
1109461,
1128121,
1132657,
1139281,
1141141,
1145257,
1152271,
1157689,
1168513,
1193221,
1194649,
1207361,
1246785,
1251949,
1252697,
1275681,
1277179,
1293337,
1302451,
1306801,
1325843,
1333333,
1357441,
1357621,
1373653,
1394185,
1397419,
1398101,
1419607,
1433407,
1441091,
1457773,
1459927,
1461241,
1463749,
1472065,
1472353,
1472505,
1485177,
1489665,
1493857,
1500661,
1507561,
1507963,
1509709,
1520905,
1529185,
1530787,
1533601,
1533961,
1534541,
1537381,
1549411,
1569457,
1579249,
1584133,
1608465,
1615681,
1620385,
1643665,
1678541,
1690501,
1711381,
1719601,
1730977,
1735841,
1746289,
1755001,
1773289,
1801969,
1809697,
1811573,
1815465,
1826203,
1827001,
1830985,
1837381,
1839817,
1840357,
1857241,
1876393,
1892185,
1896961,
1907851,
1908985,
1909001,
1937881,
1969417,
1987021,
1993537,
1994689,
2004403,
2008597,
2035153,
2077545,
2081713,
2085301,
2089297,
2100901,
2113665,
2113921,
2121301,
2134277,
2142141,
2144521,
2162721,
2163001,
2165801,
2171401,
2181961,
2184571,
2205967,
2213121,
2232865,
2233441,
2261953,
2264369,
2269093,
2284453,
2288661,
2290641,
2299081,
2304167,
2313697,
2327041,
2350141,
2387797,
2414001,
2419385,
2433601,
2434651,
2455921,
2487941,
2491637,
2503501,
2508013,
2510569,
2513841,
2528921,
2531845,
2537641,
2603381,
2609581,
2615977,
2617451,
2626177,
2628073,
2649029,
2649361,
2670361,
2704801,
2719981,
2722681,
2746477,
2746589,
2748023,
2757241,
2773981,
2780731,
2793351,
2797921,
2811271,
2827801,
2867221,
2880361,
2882265,
2899801,
2909197,
2921161,
2940337,
2944261,
2953711,
2976487,
2977217,
2987167,
3020361,
3048841,
3057601,
3059101,
3073357,
3090091,
3094273,
3116107,
3125281,
3146221,
3165961,
3181465,
3186821,
3224065,
3225601,
3235699,
3316951,
3336319,
3337849,
3345773,
3363121,
3370641,
3375041,
3375487,
3400013,
3413533,
3429037,
3435565,
3471071,
3539101,
3542533,
3567481,
3568661,
3581761,
3605429,
3656449,
3664585,
3679201,
3726541,
3746289,
3755521,
3763801,
3779185,
3814357,
3828001,
3898129,
3911197,
3916261,
3936691,
3985921,
4005001,
4014361,
4025905,
4038673,
4069297,
4072729,
4082653,
4097791,
4101637,
4151869,
4154161,
4154977,
4181921,
4188889,
4209661,
4229601,
4259905,
4314967,
4335241,
4360621,
4361389,
4363261,
4371445,
4415251,
4463641,
4469471,
4480477,
4502485,
4504501,
4513841,
4535805,
4567837,
4613665,
4650049,
4670029,
4682833,
4698001,
4706821,
4714201,
4767841,
4806061,
4827613,
4835209,
4863127,
4864501,
4868701,
4869313,
4877641,
4895065,
4903921,
4909177,
4917331,
4917781,
4922413,
4974971,
4984001,
5016191,
5031181,
5034601,
5044033,
5049001,
5095177,
5131589,
5133201,
5148001,
5173169,
5173601,
5176153,
5187637,
5193721,
5250421,
5256091,
5258701,
5271841,
5284333,
5310721,
5351537,
5400489,
5423713,
5444489,
5456881,
5481451,
5489121,
5489641,
5524693,
5529745,
5545145,
5551201,
5560809,
5575501,
5590621,
5599765,
5632705,
5672041,
5681809,
5733649,
5758273,
5766001,
5804821,
5859031,
5872361,
5919187,
5968261,
5968873,
5977153,
6027193,
6049681,
6054985,
6118141,
6122551,
6135585,
6140161.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 1801533 values, from 341 to 999994510007533).
n\r | 0 | 1 |
2 | 0 | 1801533 | 2 |
3 | 20607 | 1547871 | 233055 | 3 |
4 | 0 | 1603709 | 0 | 197824 | 4 |
5 | 69477 | 1123305 | 224513 | 212523 | 171715 | 5 |
6 | 0 | 1547871 | 0 | 20607 | 0 | 233055 | 6 |
7 | 119752 | 807226 | 160842 | 193593 | 156600 | 180257 | 183263 | 7 |
8 | 0 | 1090108 | 0 | 98976 | 0 | 513601 | 0 | 98848 | 8 |
9 | 0 | 1004546 | 77457 | 10260 | 271353 | 77914 | 10347 | 271972 | 77684 | 9 |
10 | 0 | 1123305 | 0 | 212523 | 0 | 69477 | 0 | 224513 | 0 | 171715 | 10 |
11 | 124905 | 499651 | 124085 | 124310 | 122804 | 137240 | 130377 | 132477 | 140367 | 116455 | 148862 |
A pictorial representation of the table above
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.