Search a number
Poulet numbers
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 
201801533 2 
3206071547871233055 3 
4016037090197824 4 
5694771123305224513212523171715 5 
6015478710206070233055 6 
7119752807226160842193593156600180257183263 7 
8010901080989760513601098848 8 
9010045467745710260271353779141034727197277684 9 
1001123305021252306947702245130171715 10 
11124905499651124085124310122804137240130377132477140367116455148862

A pictorial representation of the table above
motab
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.