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evil n.  and  pronic n.

First numbers that belong to both sets:

6, 12, 20, 30, 72, 90, 132, 156, 210, 240, 272, 306, 380, 420, 462, 600, 650, 756, 870, 1056, 1122, 1260, 1406, 1482, 1560, 1806, 1892, 1980, 2070, 2256, 2352, 2550, 2652, 3192, 3422, 3660, 3906, 4032, 4160, 4290, 4556, 4830, 5112, 5256, 5402, 5550, 5852, 6162, 6642, 6972, 7140, 7482, 7656, 8010, 8190, 8556, 8930, 9312, 9702, 10100, 10920, 11556, 11772, 12432, 12656, 12882, 13110, 13340, 13806, 14280, 14762, 15252, 15750, 16512, 16770, 17292, 17822, 18360, 18906, 19460, 20022, 20306, 22052, 22650, 23256, 23562, 23870, 24492, 25440, 26082, 26406, 27060, 28056, 29070, 29412, 29756, 30450, 30800, 31152, 31506, 31862, 32942, 34782, 35156, 35910, 36672, 37056, 37830, 38612, 39006, 40200, 41006, 41412, 41820, 44310, 44732, 45156, 46010, 46440, 46872, 47306, 48180, 49506, 50400, 52212, 54522, 54990, 55932, 57360, 57840, 58806, 59292, 60762, 61752, 62750, 63756, 64770, 65280, 65792, 66306, 67340, 68382, 69432, 70490, 72092, 72630, 73712, 74256, 74802, 75350, 75900, 78120, 78680, 79242, 79806, 80372, 80940, 81510, 82656, 83810, 84390, 84972, 85556, 86730, 88506, 89102, 90300, 90902, 93330, 93942, 95790, 97032, 98910, 100172, 100806, 101442, 103362, 104006, 104652, 105950, 109230, 109892, 110556, 111222, 111890, 112560, 113232, 114582, 115260, 115940, 116622, 118680, 119370, 120062, 121452, 122150, 122850, 124256, 127806, 129240, 131406, 132132, 133590, 135792, 138012, 138756, 139502, 141752, 142506, 144780, 146306, 147840, 149382, 150932, 151710, 154056, 154842, 156420, 157212, 158802, 159600, 161202, 162006, 163620, 166056, 167690, 170156, 172640, 174306, 175142, 180200, 183612, 184470, 188790, 189660, 191406, 193160, 194040, 197580, 198470, 200256, 201152, 202950, 203852, 205662, 206570, 210222, 211140, 212060, 212982, 213906, 214832, 215760, 216690, 217622, 220430, 222312, 225150, 226100, 227052, 230880, 231842, 232806, 233772, 234740, 240590, 242556, 243542, 245520, 247506, 250500, 251502, 253512, 255530, 257556, 259590, 262656, 263682, 265740, 267806.

Some larger examples :