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interprime n.  and  super-d n.

First numbers that belong to both sets:

69, 81, 105, 231, 334, 348, 381, 462, 810, 944, 969, 1036, 1050, 1056, 1062, 1066, 1190, 1281, 1377, 1431, 1556, 1569, 1581, 1616, 1681, 1869, 2028, 2046, 2148, 2310, 2470, 2475, 2619, 2627, 2667, 3081, 3219, 3258, 3310, 3321, 3326, 3330, 3337, 3345, 3353, 3360, 3366, 3372, 3381, 3390, 3480, 3531, 4016, 4076, 4119, 4131, 4256, 4594, 4638, 4731, 4755, 4807, 5031, 5110, 5169, 5349, 5481, 5577, 5631, 5649, 5739, 5781, 5810, 6009, 6096, 6214, 6219, 6471, 6566, 6690, 6792, 6831, 6969, 7182, 7190, 7381, 7539, 7646, 7820, 7826, 7835, 7881, 8097, 8169, 8253, 8703, 8725, 8781, 8838, 8855, 8877, 8931, 9012, 9144, 9193, 9416, 9569, 9669, 9727, 9831, 10038, 10146, 10179, 10269, 10281, 10302, 10363, 10431, 10493, 10500, 10507, 10521, 10530, 10545, 10563, 10578, 10593, 10599, 10604, 10610, 10620, 10629, 10635, 10645, 10654, 10660, 10665, 10677, 10689, 10700, 10710, 10717, 10731, 10776, 10944, 11319, 11469, 11494, 11619, 11667, 11781, 11810, 11900, 12046, 12131, 12219, 12252, 12494, 12606, 12693, 12700, 12708, 12981, 13035, 13419, 13431, 13493, 13623, 13881, 14004, 14031, 14526, 14535, 14540, 14546, 14624, 14631, 14769, 14781, 15190, 15310, 15367, 15441, 15519, 15592, 15648, 15669, 15681, 16004, 16119, 16162, 16191, 16310, 16419, 16588, 16761, 16817, 16826, 16837, 16881, 17031, 17190, 17208, 17319, 17469, 17642, 17695, 18069, 18083, 18231, 18347, 18369, 18471, 18519, 18531, 18605, 19005, 19011, 19281, 19419, 19431, 19519, 19698, 19890, 20115, 20278, 20310, 20379, 20460, 20481, 20619, 20781, 21381, 21474, 21519, 21810, 21819, 21861, 21887, 21969, 22034, 22057, 22131, 22281, 22325, 22386, 22569, 22616, 22641, 22674, 22719, 23019, 23058, 23181, 23239, 23631, 23688, 23730, 23781, 24127, 24399, 24416, 24471, 24627, 24703, 24721, 24741, 24756, 24765, 24774, 24787, 24796, 24831, 24969, 25022, 25119, 25281, 25431, 25569, 25581.

Some larger examples :