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frugal n.  and  hoax n.

First numbers that belong to both sets:

2401, 10240, 10375, 10624, 16000, 25000, 36015, 39601, 100864, 102400, 102625, 104875, 105728, 107392, 109312, 112128, 118375, 118912, 120771, 120832, 122875, 125625, 125824, 127232, 130321, 130816, 141568, 143641, 151389, 160000, 173824, 201433, 239104, 250000, 252105, 260253, 303616, 331264, 362313, 403125, 414208, 414613, 423424, 451072, 454167, 546121, 740625, 803125, 1001646, 1003648, 1004875, 1008693, 1012683, 1013750, 1018375, 1019648, 1024000, 1025285, 1027375, 1029625, 1031250, 1031744, 1033984, 1035904, 1036375, 1040625, 1042432, 1042816, 1045375, 1046272, 1047515, 1047781, 1052433, 1053808, 1054336, 1056875, 1059723, 1061248, 1062153, 1062656, 1070464, 1070625, 1071872, 1072845, 1073247, 1082109, 1088462, 1091840, 1092625, 1093504, 1100737, 1102059, 1103875, 1105454, 1105664, 1109129, 1109248, 1115370, 1116585, 1119015, 1122304, 1128625, 1130368, 1130752, 1134976, 1138125, 1138455, 1140475, 1141399, 1146625, 1147446, 1148750, 1150935, 1152256, 1153024, 1153375, 1155712, 1156466, 1157307, 1159110, 1159424, 1160704, 1160960, 1161783, 1162752, 1170176, 1171375, 1172232, 1172611, 1174144, 1174207, 1180928, 1181056, 1182625, 1184512, 1184875, 1191625, 1192401, 1198375, 1198563, 1201216, 1201250, 1202875, 1203125, 1205625, 1222528, 1223936, 1225216, 1225375, 1225625, 1226752, 1229875, 1231744, 1233664, 1235045, 1238272, 1238656, 1238750, 1247872, 1249263, 1252096, 1259392, 1261696, 1262641, 1270528, 1273344, 1283429, 1292401, 1302784, 1305619, 1313536, 1314873, 1316096, 1319247, 1324288, 1326921, 1330425, 1331456, 1336466, 1356544, 1363712, 1364375, 1372160, 1372707, 1376109, 1378048, 1381455, 1385216, 1390173, 1406727, 1408125, 1411584, 1416447, 1420032, 1435904, 1439232, 1441875, 1447065, 1453312, 1465088, 1465385, 1471232, 1474048, 1475625, 1476352, 1481135, 1483264, 1499911, 1503488, 1514752, 1517341, 1522176, 1535744, 1539328, 1543125, 1550000, 1553377, 1571584, 1582336, 1589504, 1591407, 1600000, 1603125, 1621504, 1623125, 1625344, 1631502, 1632256, 1632512, 1632589, 1632693, 1644375, 1651671, 1663744, 1665393, 1673541, 1679104, 1697024, 1704811, 1711250, 1715000, 1721517, 1732864, 1734208, 1750784, 1761536, 1763072, 1774304, 1775115, 1784251, 1786624, 1803515, 1812736, 1822016, 1827015, 1851171, 1924993, 1940645, 1944064, 1946430, 1961728, 2000896, 2004699, 2025162, 2040625, 2050624, 2053125, 2060154, 2097819, 2110269, 2110479, 2118494, 2129344, 2144375, 2152507, 2176065, 2182626, 2220544, 2220925, 2240133.

Some larger examples :