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pronic numbers
A number of the form n(n+1). more

The first 600 pronic numbers :
2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1406, 1482, 1560, 1640, 1722, 1806, 1892, 1980, 2070, 2162, 2256, 2352, 2450, 2550, 2652, 2756, 2862, 2970, 3080, 3192, 3306, 3422, 3540, 3660, 3782, 3906, 4032, 4160, 4290, 4422, 4556, 4692, 4830, 4970, 5112, 5256, 5402, 5550, 5700, 5852, 6006, 6162, 6320, 6480, 6642, 6806, 6972, 7140, 7310, 7482, 7656, 7832, 8010, 8190, 8372, 8556, 8742, 8930, 9120, 9312, 9506, 9702, 9900, 10100, 10302, 10506, 10712, 10920, 11130, 11342, 11556, 11772, 11990, 12210, 12432, 12656, 12882, 13110, 13340, 13572, 13806, 14042, 14280, 14520, 14762, 15006, 15252, 15500, 15750, 16002, 16256, 16512, 16770, 17030, 17292, 17556, 17822, 18090, 18360, 18632, 18906, 19182, 19460, 19740, 20022, 20306, 20592, 20880, 21170, 21462, 21756, 22052, 22350, 22650, 22952, 23256, 23562, 23870, 24180, 24492, 24806, 25122, 25440, 25760, 26082, 26406, 26732, 27060, 27390, 27722, 28056, 28392, 28730, 29070, 29412, 29756, 30102, 30450, 30800, 31152, 31506, 31862, 32220, 32580, 32942, 33306, 33672, 34040, 34410, 34782, 35156, 35532, 35910, 36290, 36672, 37056, 37442, 37830, 38220, 38612, 39006, 39402, 39800, 40200, 40602, 41006, 41412, 41820, 42230, 42642, 43056, 43472, 43890, 44310, 44732, 45156, 45582, 46010, 46440, 46872, 47306, 47742, 48180, 48620, 49062, 49506, 49952, 50400, 50850, 51302, 51756, 52212, 52670, 53130, 53592, 54056, 54522, 54990, 55460, 55932, 56406, 56882, 57360, 57840, 58322, 58806, 59292, 59780, 60270, 60762, 61256, 61752, 62250, 62750, 63252, 63756, 64262, 64770, 65280, 65792, 66306, 66822, 67340, 67860, 68382, 68906, 69432, 69960, 70490, 71022, 71556, 72092, 72630, 73170, 73712, 74256, 74802, 75350, 75900, 76452, 77006, 77562, 78120, 78680, 79242, 79806, 80372, 80940, 81510, 82082, 82656, 83232, 83810, 84390, 84972, 85556, 86142, 86730, 87320, 87912, 88506, 89102, 89700, 90300, 90902, 91506, 92112, 92720, 93330, 93942, 94556, 95172, 95790, 96410, 97032, 97656, 98282, 98910, 99540, 100172, 100806, 101442, 102080, 102720, 103362, 104006, 104652, 105300, 105950, 106602, 107256, 107912, 108570, 109230, 109892, 110556, 111222, 111890, 112560, 113232, 113906, 114582, 115260, 115940, 116622, 117306, 117992, 118680, 119370, 120062, 120756, 121452, 122150, 122850, 123552, 124256, 124962, 125670, 126380, 127092, 127806, 128522, 129240, 129960, 130682, 131406, 132132, 132860, 133590, 134322, 135056, 135792, 136530, 137270, 138012, 138756, 139502, 140250, 141000, 141752, 142506, 143262, 144020, 144780, 145542, 146306, 147072, 147840, 148610, 149382, 150156, 150932, 151710, 152490, 153272, 154056, 154842, 155630, 156420, 157212, 158006, 158802, 159600, 160400, 161202, 162006, 162812, 163620, 164430, 165242, 166056, 166872, 167690, 168510, 169332, 170156, 170982, 171810, 172640, 173472, 174306, 175142, 175980, 176820, 177662, 178506, 179352, 180200, 181050, 181902, 182756, 183612, 184470, 185330, 186192, 187056, 187922, 188790, 189660, 190532, 191406, 192282, 193160, 194040, 194922, 195806, 196692, 197580, 198470, 199362, 200256, 201152, 202050, 202950, 203852, 204756, 205662, 206570, 207480, 208392, 209306, 210222, 211140, 212060, 212982, 213906, 214832, 215760, 216690, 217622, 218556, 219492, 220430, 221370, 222312, 223256, 224202, 225150, 226100, 227052, 228006, 228962, 229920, 230880, 231842, 232806, 233772, 234740, 235710, 236682, 237656, 238632, 239610, 240590, 241572, 242556, 243542, 244530, 245520, 246512, 247506, 248502, 249500, 250500, 251502, 252506, 253512, 254520, 255530, 256542, 257556, 258572, 259590, 260610, 261632, 262656, 263682, 264710, 265740, 266772, 267806, 268842, 269880, 270920, 271962, 273006, 274052, 275100, 276150, 277202, 278256, 279312, 280370, 281430, 282492, 283556, 284622, 285690, 286760, 287832, 288906, 289982, 291060, 292140, 293222, 294306, 295392, 296480, 297570, 298662, 299756, 300852, 301950, 303050, 304152, 305256, 306362, 307470, 308580, 309692, 310806, 311922, 313040, 314160, 315282, 316406, 317532, 318660, 319790, 320922, 322056, 323192, 324330, 325470, 326612, 327756, 328902, 330050, 331200, 332352, 333506, 334662, 335820, 336980, 338142, 339306, 340472, 341640, 342810, 343982, 345156, 346332, 347510, 348690, 349872, 351056, 352242, 353430, 354620, 355812, 357006, 358202, 359400, 360600.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 31622776 values, from 2 to 999999993568952).

n\r 0  1 
2316227760 2 
321081850010540926 3 
4158113880158113880 4 
51264911063245551264911100 5 
621081850010540926000 6 
79035078090350790045175409035079 7 
879056940790569407905694079056940 8 
97027282010540926702728400702728400 9 
10126491100126491110006324555000 10 
1157495945749596574959600057495960287479857495960

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.