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gapful n.  and  sphenic n.

First numbers that belong to both sets:

105, 110, 130, 154, 165, 170, 190, 195, 231, 286, 374, 385, 561, 682, 1001, 1005, 1010, 1030, 1065, 1070, 1090, 1095, 1130, 1185, 1221, 1245, 1270, 1310, 1335, 1370, 1390, 1414, 1443, 1455, 1490, 1510, 1515, 1545, 1547, 1551, 1570, 1605, 1630, 1635, 1670, 1695, 1729, 1730, 1771, 1790, 1810, 1833, 1834, 1887, 1905, 1910, 1930, 1965, 1970, 1990, 2093, 2121, 2222, 2553, 2626, 2639, 2751, 2882, 3115, 3333, 3367, 3395, 3434, 3441, 3535, 3605, 3745, 3815, 3838, 3939, 3955, 4277, 4551, 4646, 4773, 5151, 5335, 5369, 5555, 5665, 5757, 5858, 5883, 5885, 5995, 6097, 6262, 6305, 6565, 6695, 6771, 6955, 6969, 7189, 7474, 7777, 7881, 8099, 8245, 8282, 8585, 8686, 8755, 8787, 9191, 9215, 9393, 9494, 9595, 9785, 10023, 10047, 10090, 10095, 10130, 10131, 10153, 10155, 10190, 10210, 10245, 10283, 10310, 10330, 10365, 10387, 10390, 10461, 10490, 10510, 10514, 10515, 10610, 10630, 10635, 10654, 10690, 10785, 10803, 10870, 10905, 10910, 10930, 10970, 10995, 11030, 11039, 11063, 11085, 11090, 11121, 11145, 11170, 11229, 11230, 11265, 11290, 11354, 11355, 11407, 11415, 11451, 11494, 11510, 11530, 11535, 11577, 11595, 11609, 11630, 11710, 11713, 11805, 11810, 11870, 11891, 11930, 11955, 11973, 12010, 12111, 12130, 12135, 12165, 12170, 12230, 12257, 12290, 12310, 12315, 12331, 12334, 12345, 12363, 12370, 12405, 12435, 12490, 12551, 12585, 12590, 12749, 12754, 12770, 12790, 12795, 12830, 12855, 12885, 12890, 12910, 12939, 12945, 12970, 13010, 13030, 13070, 13101, 13107, 13143, 13155, 13174, 13190, 13210, 13215, 13245, 13270, 13277, 13305, 13321, 13447, 13533, 13594, 13605, 13610, 13651, 13665, 13670, 13699, 13730, 13785, 13810, 13871, 13874, 13889, 13935, 13981, 13990, 14053, 14055, 14090, 14115, 14127, 14205, 14230, 14270, 14290, 14294, 14295, 14313, 14330, 14390, 14434, 14443, 14467, 14470, 14505, 14510, 14530, 14565.

Some larger examples :