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frugal n.  and  happy n.

First numbers that belong to both sets:

1029, 1215, 1875, 3645, 4096, 10000, 10112, 10125, 10752, 10976, 11125, 11421, 12167, 13122, 13824, 13851, 14375, 14641, 14823, 15625, 17405, 18750, 20224, 21141, 21627, 22201, 24057, 24576, 24832, 25625, 27889, 28431, 28561, 32000, 34445, 38125, 38637, 40817, 40960, 41472, 46875, 48223, 54289, 59049, 71875, 73441, 74431, 76729, 83521, 100000, 101120, 101125, 101250, 101251, 102303, 102625, 102912, 103247, 103499, 103518, 103933, 104375, 104615, 104704, 105625, 105705, 106097, 107375, 107875, 107911, 108135, 108241, 108578, 109760, 109952, 110125, 110446, 110464, 111005, 111250, 111392, 111537, 112023, 112995, 113024, 113375, 113408, 113627, 114453, 115943, 116125, 116162, 117632, 118016, 118459, 118803, 120625, 120787, 120832, 121014, 121203, 121670, 121984, 122317, 122713, 123125, 123201, 123823, 124625, 125056, 126025, 126603, 131220, 131726, 132921, 133125, 134375, 134456, 135351, 135625, 136171, 137216, 137543, 137677, 137728, 139523, 140211, 140625, 143641, 143750, 145664, 146071, 146176, 146410, 148519, 149504, 150625, 152635, 154007, 155648, 156025, 156250, 157323, 157609, 159375, 159607, 160181, 160623, 161875, 162867, 163296, 164025, 167041, 170569, 171315, 173563, 178929, 179456, 180075, 180625, 180989, 182979, 184064, 185761, 186517, 187500, 187648, 190269, 190333, 191051, 192000, 194045, 195167, 196249, 197173, 197559, 197589, 198125, 201341, 201447, 202240, 202612, 204085, 205057, 205578, 205625, 207104, 210176, 210625, 212139, 212317, 212629, 214083, 214326, 218489, 218491, 219488, 220549, 220672, 223074, 225536, 226981, 227529, 229709, 230121, 230839, 231125, 231822, 232192, 232211, 233227, 234256, 235264, 236196, 237917, 240267, 240813, 241081, 241664, 245248, 245673, 245760, 248320, 249856, 250047, 250625, 253125, 253265, 254043, 256250, 257593, 257762, 259375, 263125, 263169, 264191, 265625, 266511, 267543, 268912, 269941, 271875, 278173, 280000, 280625, 282123, 283581, 284375, 285610, 288463, 288923, 292681, 293077, 297472, 299008, 300763, 303616, 304175, 308367, 310784, 311101, 314375, 314411, 315625, 317057, 317115, 320000, 320031, 324405, 325625, 329315, 332929, 337561, 339913, 339968, 340603, 341446, 347648, 351122, 352256.

Some larger examples :