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octagonal n.  and  unprimeable n.

First numbers that belong to both sets:

1680, 3816, 5720, 6816, 7400, 11408, 12936, 13736, 16280, 17176, 18565, 19040, 20008, 25208, 31008, 32240, 34776, 40136, 42245, 44408, 46625, 47376, 48896, 58520, 62785, 67200, 72696, 84336, 85345, 88408, 92576, 95765, 99008, 103416, 110208, 112520, 117216, 119600, 122008, 126896, 131880, 142136, 155496, 156865, 163800, 175208, 181056, 185505, 190008, 196096, 199176, 205408, 208560, 211736, 216545, 218160, 226325, 234640, 241400, 251720, 269400, 276640, 278465, 291408, 295160, 302736, 310408, 314280, 326040, 330008, 334000, 336005, 346120, 350208, 362616, 364705, 366800, 371008, 392408, 396760, 401136, 405536, 414408, 423376, 427896, 430165, 437008, 446216, 460208, 467285, 484008, 488840, 508408, 518336, 525845, 528360, 533408, 543576, 564200, 566805, 577285, 579920, 585208, 590520, 595856, 612008, 622896, 639408, 644960, 656136, 667408, 673080, 687365, 690240, 696008, 701800, 704705, 707616, 713456, 719320, 731120, 743016, 746005, 749000, 761040, 764065, 773176, 779280, 785408, 797736, 807045, 810160, 835296, 841640, 848008, 857605, 870485, 880208, 886720, 889985, 899816, 913008, 919640, 922965, 932976, 939680, 946408, 953160, 956545, 959936, 966736, 987280, 990725, 994176, 1022000, 1036056, 1039585, 1043120, 1050208, 1057320, 1064456, 1071616, 1086008, 1100496, 1122408, 1133445, 1159408, 1166880, 1170625, 1174376, 1189440, 1197008, 1212216, 1227520, 1235208, 1262305, 1266200, 1274008, 1281840, 1289696, 1305480, 1313408, 1325345, 1341345, 1353408, 1361480, 1365525, 1369576, 1377696, 1406305, 1418656, 1422785, 1447685, 1451856, 1485440, 1493896, 1502376, 1519408, 1527960, 1553760, 1562408, 1571080, 1579776, 1588496, 1623616, 1650208, 1659120, 1686000, 1695008, 1708565, 1713096, 1740408, 1772545, 1786408, 1800325, 1814296, 1818965, 1823640, 1842400, 1847105, 1851816, 1889720, 1918400, 1928008, 1942465, 1947296, 1961825, 1976408, 2055096, 2075008, 2095016, 2105056, 2110085, 2125208, 2135320, 2145456, 2160705, 2176008, 2186240, 2206776, 2217080, 2237760, 2268960, 2289880, 2316165, 2332008, 2401285, 2406656, 2439008, 2460696, 2471576, 2504360, 2526336, 2531845, 2587265, 2604008, 2620805, 2626416, 2648920, 2660208, 2705600, 2717008, 2734165, 2762880, 2774408, 2791745, 2797536, 2809136, 2820760, 2832408, 2844080, 2855776, 2891008, 2902800, 2908705, 2914616, 2938320, 2950208, 2962120, 2968085.

Some larger examples :