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hexagonal n.  and  sphenic n.

First numbers that belong to both sets:

66, 190, 231, 435, 561, 861, 946, 1653, 2278, 3655, 4371, 5151, 5995, 6441, 8911, 9453, 10011, 10585, 13366, 15051, 15753, 16471, 20301, 21115, 22366, 22791, 23653, 26335, 32131, 33153, 39621, 40186, 45451, 50403, 54946, 62481, 69751, 72771, 77421, 80601, 83845, 93961, 99235, 102831, 115921, 125751, 137026, 144453, 149878, 153181, 159895, 180901, 190653, 200661, 205761, 213531, 229503, 239086, 243253, 251695, 257403, 277885, 289941, 310078, 314821, 334153, 337431, 344035, 364231, 374545, 411778, 417241, 424581, 435711, 439453, 443211, 473851, 477753, 509545, 521731, 534061, 542361, 552826, 571915, 584821, 624403, 631126, 637885, 646953, 651511, 686206, 697971, 712221, 795691, 826255, 836571, 841753, 867903, 905185, 926841, 943251, 982101, 1004653, 1027461, 1033203, 1073845, 1091503, 1109305, 1127251, 1145341, 1172746, 1181953, 1276003, 1301691, 1347261, 1393615, 1440753, 1468041, 1474903, 1485226, 1516411, 1551441, 1558495, 1579753, 1601155, 1622701, 1658931, 1688203, 1725153, 1743778, 1762503, 1792671, 1807851, 1884711, 1963171, 2023066, 2083861, 2108431, 2158003, 2166321, 2170486, 2208151, 2233441, 2318781, 2336041, 2362051, 2379471, 2458653, 2467531, 2503203, 2521135, 2534626, 2548153, 2575315, 2584401, 2602621, 2630071, 2639253, 2657665, 2722611, 2755378, 2788341, 2812006, 2826253, 2835771, 2854855, 2960961, 2970703, 3029491, 3044278, 3118753, 3168903, 3178981, 3321753, 3332071, 3394315, 3467661, 3488761, 3520531, 3531153, 3584503, 3616705, 3627471, 3665278, 3681541, 3703281, 3730546, 3736011, 3757911, 3812941, 3857253, 3924201, 3929806, 4014361, 4048435, 4186171, 4209351, 4326211, 4361581, 4397095, 4414906, 4420851, 4432753, 4504501, 4760155, 4797253, 4834495, 4859403, 4871881, 4909411, 4921953, 5022865, 5060971, 5080078, 5099221, 5253661, 5357901, 5449951, 5469778, 5569453, 5690251, 5730805, 5771503, 5825991, 5894461, 5990991, 6018715, 6102271, 6144265, 6228685, 6292378, 6327903, 6456621, 6485401, 6528691, 6615703, 6637546, 6703291, 6747301, 6762003, 6820971, 6850551, 7134753, 7195321, 7424731, 7471045, 7517503, 7533021, 7564105, 7610851, 7634278, 7673403, 7728346, 7830903, 7894351, 7942105, 7990003, 8134561, 8207326, 8378371, 8427565, 8625781, 8809503, 8826301, 9003646, 9046131, 9165621, 9182755, 9234253, 9337681, 9520066, 9669003, 9704215, 9739491, 9934653, 10131751, 10185841, 10276311, 10294453, 10458451.

Some larger examples :