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frugal n.  and  Zuckerman n.

First numbers that belong to both sets:

128, 1715, 11664, 12288, 13824, 21248, 23328, 34992, 93312, 112128, 119313, 121344, 124416, 131712, 139968, 141824, 144128, 163296, 186624, 212224, 221184, 248832, 442368, 688128, 1114112, 1124224, 1141248, 1142144, 1161216, 1181184, 1191915, 1223424, 1242624, 1264128, 1264896, 1329696, 1389312, 1393119, 1421824, 1446336, 1492992, 1638144, 1722112, 1741824, 1778112, 1781248, 1812224, 1818112, 1818624, 1821184, 1882112, 1912896, 1936224, 1949184, 2121728, 2192832, 2228224, 2239488, 2322432, 2333772, 2426112, 2612736, 2781184, 2939328, 3219264, 3429216, 3483648, 3639168, 3981312, 4122112, 4128768, 4214784, 4644864, 4741632, 4914432, 7112448, 8142848, 9132912, 9289728, 9939915, 11112448, 11114496, 11124224, 11166336, 11183616, 11211264, 11212288, 11214848, 11217472, 11238912, 11319912, 11391111, 11412224, 11418112, 11421184, 11614464, 11911131, 11912832, 12123648, 12144128, 12192768, 12212224, 12214272, 12238848, 12282112, 12314112, 12412416, 12462336, 12474112, 12632112, 12681216, 12712448, 12812288, 12841472, 13133664, 13139496, 13146624, 13221888, 13226976, 13333248, 13392216, 13395375, 13416192, 13436928, 13492224, 13716864, 14111232, 14121216, 14183424, 14266368, 14323392, 14426112, 14819328, 14992128, 16111872, 16131312, 16146432, 16189632, 16422912, 16936128, 17421824, 18392832, 18631296, 18911232, 18942336, 19191168, 19338912, 19626624, 19922112, 21119616, 21192192, 21233664, 21282816, 21337344, 21744128, 21823488, 22127616, 22228992, 22413312, 22478848, 22742272, 23238144, 23421312, 24141824, 24198912, 24219648, 24634368, 26142912, 26313984, 26984448, 26998272, 27433728, 27869184, 27923616, 28213248, 28449792, 28711424, 29113344, 29323296, 29642112, 31186944, 31228416, 31679424, 32223744, 33312384, 33313113, 33343488, 33918912, 34111488, 34338816, 34463232, 36321696, 37449216, 38382336, 38631168, 41181696, 41222144, 41399424, 41484288, 41928192, 42239232, 42316992, 43483392, 43763328, 44122112, 44826624, 49787136, 62128128, 62332416, 66811392, 69424128, 77177744, 81616896, 82444288, 82612224, 84148224, 84229632, 88244224, 91119168, 91191339, 91611648, 91632384, 91943424, 92238912, 94182912, 94224384, 96671232, 111111424, 111111993, 111131136, 111131919, 111186432, 111192912, 111221248, 111222272, 111311739, 111321216, 111421184, 111642624, 111822336, 111878144, 111912192, 111921912, 112112128, 112122112, 112126464, 112141824, 112181248, 112192128, 112212224, 112218112, 112218624, 112243968, 112282112, 112326912, 112347648, 112624128, 112643136, 112711424, 112816128, 112828416, 113129136, 113232384, 113234112, 113327424, 113481216, 114141184, 114633792, 114642432, 114891264, 116111232, 116142336, 116212224, 116383392, 116391168, 117391113, 118132992, 118319616, 118423296, 118682112.

Some larger examples :