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octagonal n.  and  wasteful n.

First numbers that belong to both sets:

8, 40, 65, 96, 176, 225, 280, 341, 408, 481, 560, 645, 736, 833, 936, 1045, 1160, 1680, 1976, 2296, 2465, 2640, 2821, 3201, 3400, 3605, 3816, 4033, 4256, 4485, 4720, 4961, 5208, 5461, 5720, 5985, 6256, 6533, 6816, 7105, 7400, 7701, 8008, 8321, 8640, 8965, 9296, 9633, 9976, 10680, 11408, 11781, 12545, 12936, 13736, 14145, 14560, 15408, 16280, 16725, 17176, 17633, 18096, 19040, 20008, 20501, 21000, 21505, 22533, 23056, 24120, 24661, 25208, 25761, 26320, 26885, 27456, 28616, 29205, 29800, 30401, 31008, 31621, 32240, 32865, 33496, 34133, 34776, 35425, 36080, 36741, 37408, 38081, 38760, 40136, 40833, 41536, 42245, 42960, 43681, 44408, 45141, 45880, 47376, 48133, 49665, 50440, 51221, 52008, 52801, 53600, 54405, 55216, 56033, 56856, 57685, 58520, 59361, 60208, 61061, 61920, 62785, 63656, 64533, 65416, 66305, 67200, 68101, 69008, 69921, 70840, 71765, 72696, 73633, 74576, 75525, 76480, 77441, 78408, 79381, 80360, 81345, 82336, 83333, 84336, 85345, 86360, 87381, 88408, 89441, 90480, 91525, 92576, 93633, 94696, 95765, 96840, 97921, 99008, 101200, 103416, 104533, 105656, 106785, 107920, 112520, 113685, 114856, 116033, 117216, 118405, 119600, 122008, 124440, 126896, 128133, 129376, 131880, 134408, 135681, 139536, 140833, 142136, 143445, 144760, 146081, 147408, 148741, 151425, 152776, 155496, 156865, 158240, 159621, 161008, 162401, 163800, 165205, 166616, 169456, 170885, 172320, 173761, 175208, 178120, 181056, 182533, 184016, 185505, 187000, 190008, 191521, 193040, 194565, 199176, 200725, 202280, 203841, 205408, 208560, 210145, 211736, 213333, 214936, 216545, 218160, 221408, 223041, 224680, 226325, 227976, 231296, 232965, 234640, 238008, 239701, 241400, 243105, 244816, 248256, 249985, 251720, 253461, 255208, 258720, 262256, 264033, 265816, 267605, 269400, 271201, 273008, 274821, 276640, 278465, 280296, 283976, 285825, 287680, 289541, 291408, 295160, 297045, 298936, 300833, 302736, 304645, 308481, 310408, 312341, 314280, 316225, 318176, 320133, 322096, 324065, 326040, 330008, 332001, 334000.

Some larger examples :