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Duffinian n.  and  practical n.

First numbers that belong to both sets:

4, 8, 16, 32, 36, 64, 100, 128, 144, 256, 324, 392, 400, 512, 576, 784, 800, 900, 968, 1024, 1296, 1352, 1600, 1936, 2048, 2304, 2500, 2704, 2916, 3136, 3600, 3872, 4096, 4356, 4624, 5184, 5408, 5776, 6272, 6400, 7744, 8100, 8192, 8464, 9216, 9248, 10000, 10404, 10816, 11552, 11664, 12100, 12800, 13456, 14400, 15488, 16384, 16900, 16928, 17424, 18496, 19044, 19208, 19600, 20000, 20736, 21632, 22500, 23104, 25088, 25600, 26244, 26912, 28900, 30276, 30752, 30976, 32400, 32768, 33856, 36100, 36864, 38416, 40000, 41616, 43264, 43808, 46208, 46656, 48400, 50176, 52900, 53792, 53824, 57600, 59168, 60516, 61504, 62500, 65536, 66248, 67600, 67712, 69696, 70688, 72900, 73984, 76176, 78400, 79524, 82944, 84100, 86528, 87616, 89888, 90000, 92416, 93636, 96800, 101124, 102400, 104976, 107584, 107648, 108900, 111392, 113288, 115600, 117128, 118336, 119072, 121104, 123008, 123904, 125316, 129600, 131072, 132496, 135200, 135424, 136900, 141376, 144400, 147456, 147968, 153664, 160000, 163592, 166464, 168100, 171396, 173056, 175232, 179776, 181476, 184832, 184900, 186624, 193600, 200704, 202500, 204800, 211600, 215168, 215296, 220900, 222784, 226576, 228488, 230400, 231200, 234256, 236196, 236672, 238144, 242064, 246016, 247808, 248004, 250000, 260100, 262144, 270400, 270848, 272484, 278784, 279752, 280900, 282752, 285156, 287296, 288800, 291600, 295936, 304704, 307328, 318096, 320000, 322624, 327184, 329672, 331776, 336400, 341056, 345744, 348100, 350464, 352836, 359552, 360000, 369664, 372100, 374544, 376712, 390728, 399424, 401408, 404496, 409600, 419904, 422500, 423200, 430336, 430592, 435600, 440896, 445568, 448900, 456976, 462400, 468512, 473344, 476100, 476288, 484416, 488072, 490000, 495616, 500000, 501264, 504100, 506944, 512072, 518400, 524288, 527076, 529984, 532900, 544644, 547600, 559504, 562500, 565504, 574592, 577600, 589824, 591872, 602176, 624100, 627200, 640000, 645248, 652864, 654368, 656100, 658952, 659344, 665856, 672400, 672800, 678976, 682112, 685584, 688900, 692224, 700928, 715208, 715716, 719104, 722500.

Some larger examples :