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wasteful n.  and  Zuckerman n.

First numbers that belong to both sets:

4, 6, 8, 9, 12, 24, 36, 132, 144, 212, 216, 312, 315, 432, 612, 624, 672, 735, 816, 1111, 1112, 1116, 1131, 1176, 1197, 1212, 1311, 1332, 1416, 1575, 2112, 2232, 3111, 3132, 3168, 3171, 3276, 3312, 3915, 4112, 4224, 4416, 6624, 7112, 7119, 8112, 8832, 9315, 9612, 11112, 11115, 11133, 11172, 11212, 11232, 11331, 11424, 12132, 12216, 12312, 12432, 12712, 12768, 13113, 13131, 13212, 13248, 13272, 13311, 13932, 14112, 14144, 16224, 16416, 16632, 17115, 17136, 19116, 21112, 21132, 21216, 21312, 21672, 22176, 23112, 24112, 24912, 26136, 26712, 27132, 31113, 31131, 31212, 31311, 32112, 32172, 32616, 32832, 33111, 33264, 34272, 35175, 37212, 38112, 41112, 41232, 41616, 42192, 42336, 42432, 42624, 42912, 43632, 51975, 61344, 61824, 62112, 64128, 66312, 71232, 71316, 72128, 73332, 77175, 77616, 81216, 81312, 82112, 83232, 86112, 89712, 91728, 92232, 93744, 111111, 111112, 111135, 111168, 111195, 111212, 111216, 111264, 111272, 111312, 111315, 111432, 111612, 112112, 112116, 112224, 112416, 113112, 113184, 113292, 113328, 113616, 113715, 114192, 114312, 114624, 114816, 114912, 116112, 116172, 116316, 117264, 117432, 117936, 119115, 121112, 121116, 121392, 121716, 121932, 123264, 123732, 126432, 131112, 131733, 134112, 136224, 139212, 141112, 141192, 141216, 143112, 147112, 149112, 161112, 161136, 164112, 167328, 171612, 172116, 173313, 175175, 177135, 177184, 179424, 182112, 183312, 191115, 192132, 193212, 194112, 196128, 197316, 211112, 211116, 211176, 212112, 213192, 217112, 219132, 219744, 221112, 221232, 222112, 222192, 231264, 231336, 232128, 232416, 234432, 237132, 241632, 242112, 261216, 266112, 272832, 291168, 293112, 294192, 311112, 311115, 311328, 311472, 312336, 312732, 313173, 313416, 313632, 316116, 317331, 321192, 331317, 331344, 336312, 338112, 341112, 341712, 344736, 371112, 371175, 373212, 381312, 411112, 411192, 411216, 411264, 411312, 411912, 412112, 412416, 413112, 414112, 416112, 417312, 418112, 419112, 422112, 431112, 431136, 434112, 437472, 438912, 441216, 441312, 442112, 442176.

Some larger examples :