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apocalyptic n.  and  sphenic n.

First numbers that belong to both sets:

222, 285, 286, 366, 434, 506, 582, 610, 646, 822, 826, 861, 894, 970, 994, 1002, 1065, 1086, 1090, 1102, 1105, 1158, 1162, 1166, 1194, 1245, 1246, 1265, 1270, 1281, 1298, 1310, 1338, 1374, 1394, 1434, 1435, 1490, 1495, 1510, 1515, 1562, 1578, 1586, 1626, 1630, 1634, 1653, 1670, 1695, 1743, 1758, 1798, 1802, 1833, 1855, 1866, 1885, 1887, 1910, 1946, 1947, 1990, 2001, 2006, 2015, 2054, 2055, 2067, 2074, 2114, 2118, 2134, 2158, 2163, 2185, 2202, 2222, 2238, 2242, 2247, 2265, 2270, 2274, 2278, 2290, 2294, 2298, 2301, 2318, 2330, 2343, 2345, 2365, 2378, 2382, 2387, 2390, 2397, 2398, 2409, 2410, 2414, 2431, 2445, 2454, 2546, 2553, 2570, 2586, 2607, 2626, 2630, 2634, 2635, 2639, 2665, 2674, 2678, 2679, 2694, 2698, 2702, 2703, 2710, 2714, 2726, 2739, 2751, 2755, 2765, 2766, 2769, 2770, 2782, 2794, 2795, 2810, 2821, 2822, 2847, 2849, 2865, 2874, 2882, 2914, 2930, 2937, 2945, 2946, 2954, 2955, 2967, 2985, 2994, 3009, 3014, 3021, 3026, 3054, 3055, 3081, 3110, 3115, 3122, 3126, 3129, 3130, 3154, 3157, 3165, 3170, 3171, 3182, 3219, 3246, 3266, 3278, 3282, 3286, 3297, 3298, 3302, 3310, 3311, 3322, 3333, 3342, 3346, 3355, 3358, 3363, 3367, 3370, 3374, 3382, 3405, 3414, 3426, 3434, 3441, 3445, 3454, 3462, 3470, 3471, 3478, 3485, 3490, 3495, 3502, 3507, 3522, 3530, 3531, 3535, 3538, 3553, 3562, 3585, 3586, 3590, 3594, 3597, 3598, 3605, 3614, 3615, 3619, 3655, 3657, 3678, 3682, 3689, 3706, 3714, 3729, 3730, 3731, 3741, 3745, 3759, 3765, 3766, 3786, 3790, 3806, 3815, 3830, 3835, 3838, 3842, 3854, 3858, 3874, 3878, 3882, 3886, 3890, 3905, 3922, 3934, 3938, 3939, 3945, 3954, 3955, 3962, 3965, 3966, 3970, 3982, 3995, 4010, 4011, 4017, 4029, 4035, 4042, 4047.

Some larger examples :