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amenable n.  and  pronic n.

First numbers that belong to both sets:

12, 20, 56, 72, 132, 156, 240, 272, 380, 420, 552, 600, 756, 812, 992, 1056, 1260, 1332, 1560, 1640, 1892, 1980, 2256, 2352, 2652, 2756, 3080, 3192, 3540, 3660, 4032, 4160, 4556, 4692, 5112, 5256, 5700, 5852, 6320, 6480, 6972, 7140, 7656, 7832, 8372, 8556, 9120, 9312, 9900, 10100, 10712, 10920, 11556, 11772, 12432, 12656, 13340, 13572, 14280, 14520, 15252, 15500, 16256, 16512, 17292, 17556, 18360, 18632, 19460, 19740, 20592, 20880, 21756, 22052, 22952, 23256, 24180, 24492, 25440, 25760, 26732, 27060, 28056, 28392, 29412, 29756, 30800, 31152, 32220, 32580, 33672, 34040, 35156, 35532, 36672, 37056, 38220, 38612, 39800, 40200, 41412, 41820, 43056, 43472, 44732, 45156, 46440, 46872, 48180, 48620, 49952, 50400, 51756, 52212, 53592, 54056, 55460, 55932, 57360, 57840, 59292, 59780, 61256, 61752, 63252, 63756, 65280, 65792, 67340, 67860, 69432, 69960, 71556, 72092, 73712, 74256, 75900, 76452, 78120, 78680, 80372, 80940, 82656, 83232, 84972, 85556, 87320, 87912, 89700, 90300, 92112, 92720, 94556, 95172, 97032, 97656, 99540, 100172, 102080, 102720, 104652, 105300, 107256, 107912, 109892, 110556, 112560, 113232, 115260, 115940, 117992, 118680, 120756, 121452, 123552, 124256, 126380, 127092, 129240, 129960, 132132, 132860, 135056, 135792, 138012, 138756, 141000, 141752, 144020, 144780, 147072, 147840, 150156, 150932, 153272, 154056, 156420, 157212, 159600, 160400, 162812, 163620, 166056, 166872, 169332, 170156, 172640, 173472, 175980, 176820, 179352, 180200, 182756, 183612, 186192, 187056, 189660, 190532, 193160, 194040, 196692, 197580, 200256, 201152, 203852, 204756, 207480, 208392, 211140, 212060, 214832, 215760, 218556, 219492, 222312, 223256, 226100, 227052, 229920, 230880, 233772, 234740, 237656, 238632, 241572, 242556, 245520, 246512, 249500, 250500, 253512, 254520, 257556, 258572, 261632, 262656, 265740, 266772, 269880, 270920, 274052, 275100, 278256, 279312, 282492, 283556, 286760, 287832, 291060, 292140, 295392, 296480, 299756, 300852, 304152, 305256, 308580, 309692, 313040, 314160.

Some larger examples :