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gapful n.  and  pronic n.

First numbers that belong to both sets:

110, 132, 240, 462, 600, 1056, 1190, 1260, 1332, 1560, 1640, 1980, 2756, 3540, 3660, 4032, 4160, 5550, 5700, 6006, 6480, 7140, 9900, 10100, 10920, 11130, 11772, 11990, 12210, 12432, 12656, 13110, 13340, 13572, 14280, 14520, 15252, 15500, 15750, 16256, 16512, 16770, 17030, 17292, 18090, 18360, 19460, 19740, 20306, 20592, 20880, 23562, 24180, 25440, 25760, 27060, 30450, 32220, 32580, 34410, 35910, 36672, 37830, 38220, 40200, 41412, 43056, 46440, 46872, 50400, 50850, 61752, 63756, 65280, 67860, 69960, 70490, 78120, 78680, 82082, 93330, 98910, 99540, 102080, 102720, 104652, 105300, 105950, 108570, 109230, 111890, 112560, 113232, 115260, 115940, 118680, 119370, 121452, 122150, 122850, 123552, 124256, 125670, 126380, 127092, 129240, 129960, 132132, 132860, 133590, 135056, 135792, 136530, 137270, 138012, 140250, 141000, 144020, 144780, 147072, 147840, 148610, 151710, 152490, 155630, 156420, 157212, 159600, 160400, 163620, 164430, 166872, 167690, 168510, 169332, 171810, 172640, 173472, 175980, 176820, 179352, 180200, 181050, 183612, 184470, 185330, 186192, 187056, 188790, 189660, 193160, 194040, 196692, 197580, 198470, 203852, 207480, 211140, 212060, 212982, 215760, 218556, 224202, 226100, 229920, 230880, 233772, 234740, 245520, 249500, 250500, 254520, 256542, 257556, 265740, 266772, 269880, 270920, 275100, 279312, 283556, 286760, 289982, 291060, 292140, 296480, 301950, 307470, 308580, 314160, 318660, 322056, 324330, 325470, 331200, 332352, 335820, 341640, 342810, 348690, 353430, 359400, 360600, 366630, 370272, 371490, 375156, 377610, 378840, 385020, 390000, 396270, 397530, 405132, 408960, 410240, 424452, 429680, 441560, 445556, 450912, 460362, 461720, 463080, 471282, 480942, 483720, 496320, 524900, 526350, 529256, 530712, 561750, 563250, 599850, 607620, 609180, 628056, 632820, 640800, 647220, 650442, 665040, 671580, 679800, 699732, 704760, 706440, 730170, 740460, 745632, 764750, 766500, 791210, 796556, 801920, 812702, 814506, 890192, 892080, 911070, 961380, 977132, 979110, 981090, 985056, 999000, 1001000, 1009020, 1011030, 1015056, 1017072, 1019090, 1021110, 1023132, 1029210, 1031240, 1033272, 1039380, 1041420.

Some larger examples :