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balanced n.  and  sphenic n.

First numbers that belong to both sets:

42, 78, 114, 154, 165, 170, 195, 266, 290, 318, 410, 426, 434, 438, 518, 534, 555, 574, 582, 590, 595, 598, 602, 618, 651, 654, 658, 665, 678, 682, 710, 742, 782, 790, 805, 806, 894, 902, 906, 962, 970, 978, 1022, 1054, 1070, 1102, 1178, 1298, 1334, 1358, 1394, 1398, 1490, 1634, 1670, 1730, 1758, 1778, 1790, 1826, 1946, 1986, 2014, 2022, 2054, 2109, 2110, 2134, 2135, 2139, 2146, 2154, 2158, 2163, 2222, 2230, 2233, 2247, 2261, 2265, 2266, 2278, 2282, 2289, 2290, 2334, 2343, 2355, 2379, 2382, 2387, 2390, 2405, 2406, 2409, 2410, 2445, 2451, 2454, 2482, 2505, 2506, 2514, 2542, 2586, 2613, 2635, 2665, 2666, 2674, 2678, 2690, 2702, 2710, 2714, 2726, 2737, 2755, 2758, 2766, 2769, 2770, 2778, 2786, 2829, 2830, 2865, 2882, 2914, 2930, 2954, 3009, 3111, 3115, 3126, 3129, 3130, 3157, 3171, 3178, 3219, 3237, 3282, 3297, 3298, 3335, 3342, 3363, 3370, 3378, 3395, 3426, 3462, 3490, 3522, 3597, 3598, 3605, 3606, 3619, 3621, 3633, 3634, 3657, 3658, 3682, 3729, 3730, 3745, 3846, 3857, 3858, 3874, 3905, 3970, 6695, 6721, 6963, 7163, 7189, 7257, 7449, 7469, 7503, 7511, 7521, 7527, 7611, 7719, 7845, 7881, 7945, 7953, 7959, 8165, 8169, 8195, 8215, 8229, 8239, 8245, 8255, 8313, 8323, 8337, 8414, 8435, 8437, 8439, 8445, 8481, 8530, 8535, 8555, 8558, 8565, 8569, 8570, 8585, 8601, 8606, 8607, 8630, 8634, 8643, 8662, 8666, 8671, 8679, 8682, 8695, 8697, 8763, 8798, 8822, 8826, 8827, 8877, 8878, 8886, 8922, 8931, 8934, 8938, 8961, 8979, 8985, 8987, 9015, 9035, 9061, 9062, 9066, 9074, 9095, 9110, 9129, 9138, 9158, 9185, 9186, 9213, 9269, 9285, 9303, 9309, 9331, 9334, 9339, 9367, 9373, 9374, 9398, 9401, 9402, 9415, 9417, 9422, 9429, 9434.

Some larger examples :