k Values of n<=300 such that n-th square triangular number has exactly k divisors ===================== =================================================================================== 1 1 9 2, 3, 5, 29, 59 15 7 27 11, 13, 19, 47, 53, 89 45 4 81 9, 17, 23, 41, 67, 97, 257, 281 189 8 243 25, 31, 43, 61, 73, 101, 103, 131, 157, 163, 167, 173, 227 405 6 729 10, 16, 37, 71, 83, 107, 109, 113, 127, 137, 139, 149, 151, 179, 191, 239, 271, 293 1215 14, 49 2025 15, 21 2187 26, 27, 33, 58, 79, 94, 169, 181, 193, 211, 263, 277 3645 35 6075 12 6561 22, 69, 118, 121, 197, 223, 251 10935 145 18225 28 19683 34, 38, 39, 46, 82, 106, 177, 233, 241, 269, 283, 295 24057 32 32805 20, 52, 161 45927 18 59049 51, 55, 57, 141, 199, 229, 247 98415 77 137781 91 177147 50, 62, 65, 86, 87, 95, 122, 134, 143, 159, 178, 202, 209, 226, 289, 291 229635 24 295245 44, 188, 203 492075 45 531441 74, 85, 93, 115, 123, 125, 146, 218, 221, 235, 237, 267, 278, 299 688905 56 767637 64 885735 76, 119, 164 1240029 40, 104 1476225 63, 68 1594323 158, 166, 194, 206, 214, 219, 249, 265 2657205 98, 116, 133, 205, 217 4782969 81, 99, 111, 129, 155, 201, 298 6200145 36 7381125 30 7971615 48, 92, 212, 236, 253, 268, 287 11160261 88 14348907 80, 117, 183, 187, 254 18600435 147 22143375 42 23914845 128, 148, 172, 244, 259 43046721 54, 185, 208, 215, 262 71744535 112, 245 129140163 142, 207, 274 167403915 75, 136 215233605 78, 292 243931419 256 301327047 152, 184 332150625 105 358722675 66 387420489 171, 213 645700815 70, 100, 124, 138 903981141 232 1076168025 196 1162261467 153, 261 1937102445 102, 175 2367569655 96 2989355625 60 3228504075 135 3486784401 130, 176, 243, 275 4261625379 160 6327867987 72 8135830269 296 8968066875 84 10460353203 110, 242 17433922005 114, 284 24407490807 182 29056536675 165, 189 31381059609 230, 250 52301766015 154, 174, 282 63924380685 224 87169610025 156 94143178827 170, 279 156905298045 186, 190, 238, 258, 272, 290 219667417263 248 282429536481 297 435848050125 132 470715894135 222 659002251789 144, 200 784526490225 140 847288609443 286 1412147682405 108 1830561810525 90 2353579470675 231 3295011258945 273 4236443047215 246, 260 5491685431575 126 9152809052625 120 11767897353375 204 12709329141645 266 18357919871265 192 21182215236075 195, 255, 276, 285 27960524111619 162 63546645708225 228 82375281473625 168 88965303991515 198 266895911974545 225 343151886824415 220 444826519957575 150 480412641554181 234 4003438679618175 294 7206189623312715 280 8578797170610375 240 15853617171287973 288 38913423965888661 216 60051580194272625 252 108092844349690725 264 180154740582817875 180 5790688090162003125 210 101313878825474406675 270 393998417654622692625 300