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heptagonal n.  and  sphenic n.

First numbers that belong to both sets:

286, 874, 970, 1918, 3367, 3553, 4558, 6682, 8323, 8614, 11122, 11458, 12145, 14707, 16687, 17098, 17935, 18361, 19669, 21022, 27931, 30085, 33466, 38254, 42055, 42706, 44023, 44689, 46717, 48094, 50197, 55279, 61387, 64561, 73702, 79834, 81631, 82537, 85285, 88078, 89965, 92833, 101707, 105781, 108889, 110986, 114169, 117397, 128482, 135373, 141253, 148474, 157126, 159643, 160909, 175165, 176491, 180499, 192793, 199798, 204061, 209815, 214183, 226051, 227557, 232105, 235162, 244453, 250747, 258727, 270109, 275062, 298771, 300502, 303979, 316306, 327067, 332515, 341695, 349129, 354757, 371911, 387499, 407434, 411481, 425803, 436183, 438274, 457318, 468073, 476767, 487747, 496621, 503329, 521437, 542191, 549199, 551545, 558613, 577681, 580087, 601966, 606883, 609349, 629257, 646939, 659719, 667447, 683038, 685654, 690901, 701455, 730891, 741745, 747202, 763693, 772006, 774787, 788767, 800041, 831457, 843031, 860542, 866419, 902101, 950797, 956974, 966277, 978751, 985018, 988159, 1016653, 1052029, 1061782, 1065043, 1084714, 1091311, 1121245, 1144807, 1161787, 1165198, 1185769, 1192666, 1196122, 1213477, 1216963, 1227451, 1259185, 1287733, 1298521, 1309354, 1345789, 1386445, 1401379, 1420159, 1431487, 1435273, 1465741, 1477249, 1523731, 1527637, 1547242, 1559065, 1586827, 1622881, 1634989, 1643086, 1671583, 1683871, 1704451, 1708582, 1716859, 1754353, 1771147, 1779574, 1856317, 1869265, 1921507, 1925893, 1939081, 1947898, 1961161, 1974469, 1978915, 1987822, 2014663, 2028151, 2032657, 2082553, 2123827, 2142301, 2156209, 2170162, 2179489, 2250079, 2321794, 2326615, 2355646, 2370229, 2409337, 2468599, 2483527, 2528581, 2609677, 2650705, 2666173, 2671339, 2686867, 2712847, 2812711, 2860645, 2936014, 3034357, 3056431, 3073039, 3100819, 3139921, 3168001, 3190555, 3201862, 3252991, 3258697, 3275845, 3321793, 3327559, 3373867, 3379678, 3397141, 3432202, 3485131, 3520642, 3532519, 3556333, 3628255, 3676603, 3755851, 3774259, 3805039, 3823567, 3829753, 3866974, 3916882, 3954523, 4017658, 4049413, 4106887, 4164766, 4184149, 4203577, 4262131, 4288285, 4340833, 4440223, 4520545, 4540738, 4547479, 4581259, 4601587, 4628761, 4710763, 4793485, 4828165, 4855999, 4869946, 4876927, 4932955, 4939981, 4961089, 4982242, 5017597, 5024683, 5081551, 5088682, 5153086, 5196247, 5319514, 5341417, 5370691, 5392699, 5451607.

Some larger examples :