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tetrahedral numbers
A figurate number of the form n(n+1)(n+2)/6. more

The first 600 tetrahedral numbers :
1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 364, 455, 560, 680, 816, 969, 1140, 1330, 1540, 1771, 2024, 2300, 2600, 2925, 3276, 3654, 4060, 4495, 4960, 5456, 5984, 6545, 7140, 7770, 8436, 9139, 9880, 10660, 11480, 12341, 13244, 14190, 15180, 16215, 17296, 18424, 19600, 20825, 22100, 23426, 24804, 26235, 27720, 29260, 30856, 32509, 34220, 35990, 37820, 39711, 41664, 43680, 45760, 47905, 50116, 52394, 54740, 57155, 59640, 62196, 64824, 67525, 70300, 73150, 76076, 79079, 82160, 85320, 88560, 91881, 95284, 98770, 102340, 105995, 109736, 113564, 117480, 121485, 125580, 129766, 134044, 138415, 142880, 147440, 152096, 156849, 161700, 166650, 171700, 176851, 182104, 187460, 192920, 198485, 204156, 209934, 215820, 221815, 227920, 234136, 240464, 246905, 253460, 260130, 266916, 273819, 280840, 287980, 295240, 302621, 310124, 317750, 325500, 333375, 341376, 349504, 357760, 366145, 374660, 383306, 392084, 400995, 410040, 419220, 428536, 437989, 447580, 457310, 467180, 477191, 487344, 497640, 508080, 518665, 529396, 540274, 551300, 562475, 573800, 585276, 596904, 608685, 620620, 632710, 644956, 657359, 669920, 682640, 695520, 708561, 721764, 735130, 748660, 762355, 776216, 790244, 804440, 818805, 833340, 848046, 862924, 877975, 893200, 908600, 924176, 939929, 955860, 971970, 988260, 1004731, 1021384, 1038220, 1055240, 1072445, 1089836, 1107414, 1125180, 1143135, 1161280, 1179616, 1198144, 1216865, 1235780, 1254890, 1274196, 1293699, 1313400, 1333300, 1353400, 1373701, 1394204, 1414910, 1435820, 1456935, 1478256, 1499784, 1521520, 1543465, 1565620, 1587986, 1610564, 1633355, 1656360, 1679580, 1703016, 1726669, 1750540, 1774630, 1798940, 1823471, 1848224, 1873200, 1898400, 1923825, 1949476, 1975354, 2001460, 2027795, 2054360, 2081156, 2108184, 2135445, 2162940, 2190670, 2218636, 2246839, 2275280, 2303960, 2332880, 2362041, 2391444, 2421090, 2450980, 2481115, 2511496, 2542124, 2573000, 2604125, 2635500, 2667126, 2699004, 2731135, 2763520, 2796160, 2829056, 2862209, 2895620, 2929290, 2963220, 2997411, 3031864, 3066580, 3101560, 3136805, 3172316, 3208094, 3244140, 3280455, 3317040, 3353896, 3391024, 3428425, 3466100, 3504050, 3542276, 3580779, 3619560, 3658620, 3697960, 3737581, 3777484, 3817670, 3858140, 3898895, 3939936, 3981264, 4022880, 4064785, 4106980, 4149466, 4192244, 4235315, 4278680, 4322340, 4366296, 4410549, 4455100, 4499950, 4545100, 4590551, 4636304, 4682360, 4728720, 4775385, 4822356, 4869634, 4917220, 4965115, 5013320, 5061836, 5110664, 5159805, 5209260, 5259030, 5309116, 5359519, 5410240, 5461280, 5512640, 5564321, 5616324, 5668650, 5721300, 5774275, 5827576, 5881204, 5935160, 5989445, 6044060, 6099006, 6154284, 6209895, 6265840, 6322120, 6378736, 6435689, 6492980, 6550610, 6608580, 6666891, 6725544, 6784540, 6843880, 6903565, 6963596, 7023974, 7084700, 7145775, 7207200, 7268976, 7331104, 7393585, 7456420, 7519610, 7583156, 7647059, 7711320, 7775940, 7840920, 7906261, 7971964, 8038030, 8104460, 8171255, 8238416, 8305944, 8373840, 8442105, 8510740, 8579746, 8649124, 8718875, 8789000, 8859500, 8930376, 9001629, 9073260, 9145270, 9217660, 9290431, 9363584, 9437120, 9511040, 9585345, 9660036, 9735114, 9810580, 9886435, 9962680, 10039316, 10116344, 10193765, 10271580, 10349790, 10428396, 10507399, 10586800, 10666600, 10746800, 10827401, 10908404, 10989810, 11071620, 11153835, 11236456, 11319484, 11402920, 11486765, 11571020, 11655686, 11740764, 11826255, 11912160, 11998480, 12085216, 12172369, 12259940, 12347930, 12436340, 12525171, 12614424, 12704100, 12794200, 12884725, 12975676, 13067054, 13158860, 13251095, 13343760, 13436856, 13530384, 13624345, 13718740, 13813570, 13908836, 14004539, 14100680, 14197260, 14294280, 14391741, 14489644, 14587990, 14686780, 14786015, 14885696, 14985824, 15086400, 15187425, 15288900, 15390826, 15493204, 15596035, 15699320, 15803060, 15907256, 16011909, 16117020, 16222590, 16328620, 16435111, 16542064, 16649480, 16757360, 16865705, 16974516, 17083794, 17193540, 17303755, 17414440, 17525596, 17637224, 17749325, 17861900, 17974950, 18088476, 18202479, 18316960, 18431920, 18547360, 18663281, 18779684, 18896570, 19013940, 19131795, 19250136, 19368964, 19488280, 19608085, 19728380, 19849166, 19970444, 20092215, 20214480, 20337240, 20460496, 20584249, 20708500, 20833250, 20958500, 21084251, 21210504, 21337260, 21464520, 21592285, 21720556, 21849334, 21978620, 22108415, 22238720, 22369536, 22500864, 22632705, 22765060, 22897930, 23031316, 23165219, 23299640, 23434580, 23570040, 23706021, 23842524, 23979550, 24117100, 24255175, 24393776, 24532904, 24672560, 24812745, 24953460, 25094706, 25236484, 25378795, 25521640, 25665020, 25808936, 25953389, 26098380, 26243910, 26389980, 26536591, 26683744, 26831440, 26979680, 27128465, 27277796, 27427674, 27578100, 27729075, 27880600, 28032676, 28185304, 28338485, 28492220, 28646510, 28801356, 28956759, 29112720, 29269240, 29426320, 29583961, 29742164, 29900930, 30060260, 30220155, 30380616, 30541644, 30703240, 30865405, 31028140, 31191446, 31355324, 31519775, 31684800, 31850400, 32016576, 32183329, 32350660, 32518570, 32687060, 32856131, 33025784, 33196020, 33366840, 33538245, 33710236, 33882814, 34055980, 34229735, 34404080, 34579016, 34754544, 34930665, 35107380, 35284690, 35462596, 35641099, 35820200, 35999900, 36180200.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 181711 values, from 1 to 999999021225736).

n\r 0  1 
213628345428 2 
3605706057160570 3 
4113569227142271422714 4 
5109026363430036342 5 
6454271514245427151434542915143 6 
7778752595902595925959025959 7 
85678411357113571135756785113571135711357 8 
9201902019120190201902019020190201902019020190 9 
1081769908600272572725727257009085 10 
11495573303916519016520001651901651933038

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.