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evil n.  and  octagonal n.

First numbers that belong to both sets:

40, 65, 96, 225, 408, 645, 736, 833, 1045, 1541, 1680, 2296, 2640, 3201, 3605, 4961, 5720, 6533, 8640, 9296, 9633, 9976, 10325, 11041, 11781, 12160, 12545, 13333, 14560, 15408, 16725, 17633, 18096, 20008, 21000, 21505, 22016, 23585, 24120, 24661, 25761, 26885, 27456, 30401, 31008, 32240, 32865, 33496, 34776, 35425, 36741, 37408, 38081, 38760, 40833, 41536, 42245, 42960, 45880, 47376, 49665, 51221, 53600, 56856, 57685, 59361, 60208, 61920, 62785, 63656, 65416, 66305, 67200, 69008, 72696, 74576, 76480, 78408, 79381, 85345, 88408, 91525, 96840, 103416, 104533, 106785, 114856, 117216, 119600, 124440, 125665, 130625, 135681, 138245, 139536, 140833, 142136, 146081, 147408, 148741, 151425, 154133, 155496, 158240, 159621, 163800, 165205, 166616, 168033, 173761, 175208, 176661, 178120, 181056, 185505, 187000, 188501, 191521, 194565, 196096, 197633, 200725, 205408, 213333, 216545, 224680, 232965, 241400, 243105, 246533, 248256, 251720, 255208, 262256, 267605, 276640, 278465, 280296, 282133, 289541, 298936, 300833, 302736, 310408, 316225, 320133, 322096, 324065, 326040, 330008, 336005, 338016, 340033, 344085, 352261, 354320, 362616, 366800, 373121, 375240, 377365, 385925, 388080, 390241, 392408, 394581, 398945, 401136, 407745, 412181, 414408, 418880, 423376, 427896, 430165, 437008, 439301, 441600, 450856, 455520, 460208, 462561, 474416, 486421, 488840, 493696, 496133, 498576, 503480, 513360, 515845, 520833, 525845, 533408, 535941, 541025, 543576, 548696, 551265, 556421, 564200, 566805, 569416, 572033, 574656, 579920, 585208, 587861, 595856, 598533, 601216, 603905, 606600, 609301, 617440, 620165, 622896, 625633, 633880, 639408, 644960, 647745, 650536, 653333, 658945, 664581, 667408, 670241, 673080, 675925, 687365, 693121, 696008, 701800, 713456, 719320, 725208, 734085, 737056, 743016, 752001, 758021, 761040, 773176, 779280, 788481, 794645, 803936, 819541, 825825, 828976, 848008, 851201, 854400, 857605, 864033, 867256, 880208, 889985, 893256, 899816, 909701, 913008, 922965, 926296, 932976, 943041, 946408, 949781, 956545, 963333, 983841, 990725, 1004565, 1008040, 1011521, 1015008, 1018501, 1025505, 1029016.

Some larger examples :