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admirable n.  and  sphenic n.

First numbers that belong to both sets:

30, 42, 66, 70, 78, 102, 114, 138, 174, 186, 222, 246, 258, 282, 318, 354, 366, 402, 426, 438, 474, 498, 534, 582, 606, 618, 642, 654, 678, 762, 786, 822, 834, 894, 906, 942, 978, 1002, 1038, 1074, 1086, 1146, 1158, 1182, 1194, 1266, 1338, 1362, 1374, 1398, 1434, 1446, 1506, 1542, 1578, 1614, 1626, 1662, 1686, 1698, 1758, 1842, 1866, 1878, 1902, 1986, 2022, 2082, 2094, 2118, 2154, 2202, 2238, 2274, 2298, 2334, 2382, 2406, 2454, 2514, 2526, 2586, 2598, 2634, 2658, 2694, 2742, 2766, 2778, 2802, 2874, 2922, 2946, 2994, 3018, 3054, 3126, 3138, 3246, 3282, 3342, 3378, 3414, 3426, 3462, 3522, 3558, 3594, 3606, 3642, 3678, 3702, 3714, 3786, 3846, 3858, 3882, 3918, 3954, 3966, 4038, 4062, 4098, 4146, 4206, 4254, 4314, 4362, 4398, 4434, 4458, 4506, 4542, 4566, 4614, 4638, 4722, 4782, 4854, 4866, 4926, 4938, 4962, 4974, 5034, 5118, 5142, 5154, 5178, 5262, 5286, 5298, 5322, 5442, 5466, 5514, 5574, 5622, 5646, 5682, 5718, 5802, 5826, 5862, 5898, 5946, 5982, 6054, 6078, 6114, 6126, 6186, 6198, 6234, 6294, 6306, 6366, 6378, 6414, 6522, 6546, 6558, 6582, 6618, 6654, 6702, 6738, 6774, 6906, 6918, 6978, 7026, 7086, 7122, 7158, 7206, 7278, 7302, 7338, 7374, 7386, 7422, 7494, 7554, 7662, 7674, 7698, 7734, 7746, 7782, 7806, 7818, 7842, 7914, 7926, 7962, 8166, 8202, 8238, 8286, 8394, 8454, 8538, 8562, 8574, 8598, 8634, 8682, 8706, 8718, 8754, 8826, 8886, 8898, 8922, 8934, 8958, 8994, 9066, 9138, 9186, 9258, 9294, 9318, 9354, 9402, 9426, 9474, 9498, 9582, 9606, 9642, 9654, 9678, 9714, 9726, 9762, 9822, 9942, 9978, 10002, 10014, 10158, 10182, 10194, 10254, 10326, 10338, 10398, 10446, 10482, 10518, 10554, 10662, 10698, 10722, 10734, 10806, 10866, 10938.

Some larger examples :