Search a number
gapful n.  and  powerful n.

First numbers that belong to both sets:

100, 108, 121, 200, 225, 400, 484, 500, 800, 900, 1000, 1125, 1152, 1296, 1331, 1600, 1728, 1764, 1800, 1936, 2000, 2025, 2187, 2304, 2500, 2700, 3456, 3600, 3872, 4000, 4608, 5000, 5184, 5400, 8000, 9000, 9025, 9216, 10000, 10125, 10368, 10584, 10800, 10816, 10976, 11025, 12100, 12168, 12348, 12500, 12544, 12800, 13068, 13456, 13500, 14112, 14400, 14641, 15376, 15552, 16000, 16200, 16875, 16900, 17689, 18000, 18225, 18252, 18432, 18496, 19600, 19773, 20000, 21025, 21125, 21168, 21600, 22500, 22707, 24025, 24200, 24300, 24336, 24389, 24500, 25000, 25088, 25600, 25947, 27000, 27225, 28125, 28224, 28800, 28900, 30276, 30625, 30752, 32400, 33075, 34596, 36000, 36992, 38988, 39304, 40000, 41209, 43200, 45000, 47089, 48400, 48600, 49000, 49392, 49923, 50000, 50176, 51200, 52900, 54000, 57600, 57800, 61504, 64800, 67500, 69192, 69696, 70756, 73008, 77175, 77976, 78400, 80000, 86400, 90000, 97200, 100000, 101761, 102400, 103684, 103788, 103968, 104329, 104976, 105800, 107653, 107811, 108000, 108900, 109512, 110592, 111132, 112500, 112896, 114075, 115200, 115600, 116281, 117612, 118336, 119025, 121000, 121032, 121500, 122500, 124416, 124848, 125000, 126736, 127008, 128000, 129600, 132300, 132496, 133100, 133128, 135000, 135200, 136125, 136900, 137200, 139392, 139968, 140625, 141376, 142884, 143748, 144000, 144400, 144500, 145800, 146016, 147456, 147852, 148176, 151875, 152100, 152352, 153664, 155952, 156800, 156816, 157216, 159048, 160000, 161051, 162000, 163216, 164025, 164268, 165375, 165888, 168100, 168200, 169000, 169344, 171500, 172800, 172872, 173056, 175616, 176400, 176868, 179776, 180000, 180500, 181548, 184041, 184900, 187272, 189225, 190096, 190125, 190512, 190969, 192200, 193600, 194400, 194688, 195075, 196000, 197136, 197568, 199692, 200000, 202500, 204800, 207025, 207368, 210125, 211600, 213867, 214375, 216000, 216225, 217800, 218700, 219024, 219700, 220500, 220900, 221184, 222264, 223587, 225000, 225625, 230400, 231125, 231200, 231525, 231868, 235224, 235225, 237276, 240100, 242000, 242064, 243000, 243049, 243675.

Some larger examples :