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happy n.  and  sphenic n.

First numbers that belong to both sets:

70, 130, 190, 230, 310, 638, 665, 790, 806, 874, 946, 970, 1030, 1090, 1158, 1182, 1185, 1209, 1221, 1222, 1258, 1281, 1309, 1335, 1353, 1390, 1474, 1533, 1547, 1578, 1581, 1582, 1599, 1670, 1742, 1758, 1771, 1902, 1930, 2091, 2093, 2109, 2118, 2121, 2158, 2185, 2211, 2242, 2338, 2390, 2422, 2485, 2542, 2555, 2586, 2630, 2639, 2658, 2685, 2714, 2715, 2717, 2751, 2755, 2847, 2865, 2874, 2919, 2930, 3002, 3026, 3130, 3206, 3310, 3346, 3355, 3367, 3382, 3531, 3535, 3553, 3605, 3634, 3670, 3689, 3706, 3731, 3766, 3790, 3806, 3830, 3913, 3926, 3962, 3970, 4090, 4118, 4147, 4255, 4366, 4558, 4582, 4585, 4715, 4718, 4782, 4807, 4814, 4870, 4906, 5066, 5118, 5133, 5174, 5178, 5181, 5217, 5254, 5271, 5282, 5286, 5306, 5335, 5542, 5555, 5558, 5605, 5630, 5682, 5695, 5718, 5781, 5798, 5811, 5817, 5822, 5826, 5842, 5845, 5862, 5871, 6035, 6055, 6083, 6094, 6170, 6202, 6285, 6293, 6302, 6305, 6307, 6335, 6346, 6398, 6409, 6530, 6582, 6634, 6643, 6665, 6730, 6789, 6830, 6923, 6955, 6978, 6987, 7090, 7158, 7185, 7306, 7366, 7390, 7414, 7474, 7521, 7574, 7598, 7599, 7610, 7689, 7698, 7815, 7842, 7869, 7887, 7958, 7959, 7973, 8018, 8074, 8099, 8115, 8174, 8215, 8218, 8245, 8323, 8414, 8455, 8517, 8555, 8562, 8630, 8679, 8697, 8769, 8787, 8810, 8877, 9021, 9070, 9129, 9159, 9195, 9219, 9291, 9331, 9362, 9370, 9519, 9579, 9591, 9597, 9638, 9678, 9698, 9737, 9785, 9795, 9915, 9951, 10090, 10114, 10158, 10182, 10209, 10222, 10257, 10258, 10274, 10281, 10330, 10366, 10373, 10390, 10518, 10574, 10706, 10742, 10745, 10754, 10785, 10930, 10959, 10995, 11077, 11082, 11085, 11134, 11145, 11174, 11194, 11202, 11229, 11234, 11238, 11342, 11415, 11431, 11446, 11451, 11455, 11501, 11510, 11546, 11554, 11595, 11618.

Some larger examples :