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sphenic n.  and  super-d n.

First numbers that belong to both sets:

105, 190, 231, 310, 318, 715, 782, 969, 1054, 1065, 1066, 1070, 1131, 1270, 1281, 1310, 1419, 1581, 1645, 1778, 1810, 1869, 1965, 2261, 2373, 2431, 2667, 2690, 2769, 2810, 2919, 2954, 3058, 3081, 3219, 3310, 3322, 3333, 3335, 3342, 3345, 3346, 3355, 3358, 3363, 3367, 3370, 3374, 3378, 3382, 3471, 3531, 3619, 3621, 3731, 3783, 3819, 3855, 4015, 4017, 4081, 4137, 4190, 4310, 4314, 4431, 4611, 4638, 4669, 4731, 4755, 4807, 4809, 4823, 4854, 4895, 4966, 5019, 5061, 5109, 5181, 5302, 5369, 5511, 5558, 5649, 5681, 5690, 5719, 5781, 6010, 6123, 6190, 6214, 6231, 6254, 6294, 6310, 6357, 6369, 6414, 6519, 6531, 6681, 6862, 6919, 6965, 6969, 6981, 7042, 7046, 7077, 7086, 7190, 7198, 7322, 7390, 7469, 7491, 7539, 7690, 7707, 7719, 7815, 7818, 7833, 7842, 7869, 7881, 7931, 7954, 8007, 8169, 8239, 8319, 8435, 8481, 8569, 8769, 8787, 8810, 8877, 8931, 9190, 9219, 9231, 9269, 9285, 9331, 9381, 9519, 9545, 9581, 9645, 9669, 9681, 9682, 9805, 9831, 9919, 10105, 10127, 10131, 10190, 10257, 10281, 10310, 10354, 10355, 10419, 10490, 10491, 10498, 10502, 10505, 10507, 10509, 10510, 10514, 10515, 10518, 10526, 10534, 10538, 10549, 10554, 10563, 10569, 10574, 10585, 10586, 10591, 10595, 10598, 10610, 10615, 10619, 10621, 10622, 10630, 10634, 10635, 10642, 10653, 10654, 10662, 10678, 10689, 10690, 10698, 10703, 10706, 10707, 10714, 10718, 10722, 11005, 11145, 11230, 11431, 11451, 11481, 11487, 11494, 11810, 11837, 11869, 11919, 11921, 11931, 11942, 12019, 12046, 12089, 12129, 12309, 12310, 12331, 12669, 12694, 12698, 12719, 13082, 13190, 13233, 13281, 13458, 13481, 13623, 13642, 13719, 13731, 13735, 13810, 13855, 13881, 13981, 14181, 14182, 14231, 14271, 14331, 14433, 14529, 14530, 14538, 14539, 14541, 14542, 14546, 14555, 14619, 14682, 14710, 14781, 14810, 14819, 14870, 14937, 15038.

Some larger examples :