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aban n.  and  frugal n.

First numbers that belong to both sets:

125, 128, 243, 256, 343, 512, 625, 729, 1000000, 1000188, 1000192, 1000309, 1000448, 1000531, 1000576, 1000625, 1000917, 1000949, 2000000, 2000033, 2000133, 2000376, 2000384, 2000619, 2000896, 3000000, 3000221, 3000227, 3000564, 3000625, 3000832, 4000000, 4000023, 4000066, 4000481, 4000752, 5000000, 5000043, 5000211, 5000704, 6000000, 6000099, 6000399, 6000625, 7000000, 7000531, 7000587, 7000885, 8000000, 8000132, 9000000, 10000000, 10000086, 10000165, 10000179, 10000422, 10000625, 10000665, 10000851, 11000000, 11000125, 11000201, 11000207, 11000320, 11000375, 11000576, 11000610, 11000625, 11000875, 12000000, 12000069, 12000125, 12000198, 12000512, 12000541, 12000798, 13000000, 13000003, 13000192, 13000319, 13000704, 13000739, 13000743, 14000000, 14000128, 14000231, 14000917, 14000931, 15000000, 15000064, 15000129, 15000147, 15000625, 15000633, 16000000, 16000064, 16000256, 16000264, 16000607, 16000625, 16000751, 16000768, 16000821, 17000000, 17000037, 17000625, 18000000, 18000128, 18000187, 18000251, 18000297, 18000625, 18000640, 18000711, 19000000, 19000064, 19000313, 19000413, 19000656, 19000870, 19000881, 19000899, 20000000, 20000115, 20000330, 20000375, 20000601, 20000844, 21000000, 21000242, 21000303, 21000625, 21000704, 21000789, 21000965, 22000000, 22000363, 22000625, 23000000, 23000193, 23000551, 23000679, 24000000, 24000005, 24000138, 24000396, 25000000, 25000215, 25000927, 26000000, 26000429, 26000879, 27000000, 27000625, 27000702, 27000832, 28000000, 28000161, 28000256, 28000462, 28000625, 29000000, 29000349, 29000993, 30000000, 30000495, 30000537, 31000000, 31000725, 32000000, 32000059, 32000128, 32000512, 32000528, 32000913, 33000000, 33000373, 34000000, 34000063, 34000561, 34000625, 35000000, 35000301, 36000000, 36000207, 36000256, 36000374, 36000594, 36000625, 37000000, 37000919, 38000000, 38000128, 38000583, 38000627, 39000000, 39000025, 39000305, 39000625, 40000000, 40000660, 41000000, 41000753, 42000000, 42000693, 43000000, 43000617, 44000000, 44000726, 45000000, 45000387, 45000441, 45000625, 45000962, 46000000, 46000601, 46000629, 46000759, 47000000, 47000817, 48000000, 48000625, 48000792, 49000000, 49000625, 49000696, 50000000, 50000825, 51000000, 51000111, 51000832, 52000000, 52000858, 53000000, 53000212, 53000249, 53000391, 54000000, 54000561, 54000891, 54000907, 55000000, 55000625, 55000863, 56000000, 56000512, 56000924, 57000000, 57000287, 58000000, 58000625, 58000827, 58000957, 59000000, 59000157, 60000000, 60000345, 60000625, 60000990, 61000000, 62000000, 62000721, 63000000, 63000909, 64000000, 64000256, 65000000, 66000000, 66000859, 67000000, 68000000, 69000000, 69000579, 70000000, 71000000, 72000000, 72000414, 73000000, 73000205, 74000000.

Some larger examples :