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frugal n.  and  tau n.

First numbers that belong to both sets:

128, 625, 1250, 2560, 6561, 10000, 10112, 10624, 11392, 12416, 13122, 16000, 17920, 21952, 26244, 31104, 32768, 35721, 43904, 50625, 52488, 57344, 62208, 64000, 69984, 80000, 98304, 100736, 101250, 102016, 103552, 103680, 103808, 104960, 105088, 105344, 105856, 106112, 107392, 108864, 109184, 109696, 109760, 109952, 110080, 110464, 112000, 112256, 112768, 113024, 113536, 116096, 116608, 117632, 117649, 118912, 119936, 120320, 120448, 121216, 121984, 123776, 124288, 125056, 125824, 126848, 127616, 131220, 131712, 135680, 150000, 151040, 155520, 156160, 163296, 163840, 164025, 170368, 171520, 172032, 174960, 181760, 183708, 186880, 192000, 202240, 209952, 212480, 217728, 219520, 227840, 229376, 235298, 240000, 245760, 248320, 262440, 279936, 280000, 281216, 286720, 294912, 311040, 320000, 321489, 328050, 349920, 360448, 367416, 393660, 425984, 435456, 448000, 489888, 491520, 497664, 524880, 557056, 559872, 560000, 622080, 622592, 628864, 642978, 653184, 688128, 708588, 753664, 768320, 793881, 839808, 875000, 877952, 878080, 884736, 941192, 950272, 960000, 979776, 1000188, 1000576, 1001344, 1002112, 1003648, 1005184, 1006976, 1007744, 1008256, 1008512, 1009024, 1009792, 1011328, 1012096, 1012500, 1013632, 1014656, 1015424, 1015808, 1015936, 1016320, 1017472, 1017728, 1019264, 1022121, 1023104, 1025152, 1025408, 1026176, 1026560, 1028992, 1030528, 1030784, 1031552, 1031744, 1032832, 1034368, 1035136, 1035392, 1035904, 1036800, 1036928, 1038208, 1038976, 1039744, 1040000, 1042816, 1044608, 1045376, 1045888, 1046912, 1047040, 1048448, 1049760, 1050000, 1050752, 1052032, 1052288, 1053568, 1053824, 1054336, 1055104, 1057280, 1057536, 1057664, 1058432, 1058841, 1058944, 1060736, 1061248, 1061504, 1062016, 1063808, 1064576, 1066112, 1069184, 1070464, 1071232, 1072000, 1072256, 1072640, 1073536, 1073792, 1076004, 1077632, 1077760, 1078144, 1078656, 1078912, 1079168, 1080704, 1081216, 1081344, 1083008, 1083681, 1083776, 1088000, 1088128, 1088640, 1089536, 1089664, 1090688, 1091456, 1092736, 1092992, 1093120, 1093504, 1096064, 1096209, 1097344, 1098368, 1100416, 1100672, 1101952, 1103360, 1103744, 1104256, 1104512, 1105024, 1106048, 1106816, 1108480, 1108809, 1108864, 1109632, 1110656, 1111168, 1112192, 1112704, 1113472, 1114112, 1114496, 1115264, 1116032, 1117568, 1118336, 1118848, 1119616, 1120384, 1121408, 1121481.

Some larger examples :