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alternating n.  and  sphenic n.

First numbers that belong to both sets:

30, 70, 78, 105, 165, 230, 238, 258, 290, 345, 385, 410, 418, 430, 434, 438, 470, 474, 494, 498, 561, 610, 618, 638, 654, 658, 670, 678, 705, 741, 814, 830, 834, 854, 874, 890, 894, 903, 969, 987, 1010, 1030, 1034, 1038, 1054, 1070, 1074, 1090, 1258, 1270, 1298, 1414, 1434, 1474, 1490, 1498, 1614, 1630, 1634, 1670, 1698, 1810, 1834, 1878, 1898, 2109, 2121, 2163, 2185, 2301, 2343, 2345, 2365, 2387, 2505, 2585, 2703, 2765, 2769, 2905, 2945, 2967, 2985, 3014, 3018, 3034, 3054, 3058, 3070, 3074, 3278, 3298, 3414, 3434, 3454, 3470, 3478, 3490, 3614, 3634, 3638, 3658, 3670, 3674, 3678, 3818, 3830, 3838, 3854, 3858, 3874, 3878, 3890, 4123, 4147, 4161, 4301, 4323, 4345, 4503, 4505, 4521, 4543, 4565, 4585, 4587, 4745, 4767, 4921, 4929, 4945, 4947, 4965, 4983, 5014, 5018, 5030, 5034, 5038, 5074, 5090, 5210, 5230, 5254, 5258, 5298, 5410, 5470, 5494, 5614, 5630, 5654, 5678, 5690, 5858, 5870, 5894, 5898, 6123, 6141, 6149, 6303, 6305, 6307, 6365, 6369, 6501, 6549, 6565, 6567, 6585, 6721, 6745, 6747, 6785, 6789, 6923, 6945, 6963, 6965, 6969, 6981, 6985, 6987, 7010, 7090, 7258, 7270, 7278, 7294, 7298, 7414, 7430, 7474, 7494, 7498, 7610, 7618, 7634, 7654, 7658, 7674, 7678, 7690, 7698, 7818, 7870, 7874, 7898, 8103, 8165, 8169, 8305, 8323, 8365, 8565, 8569, 8585, 8589, 8701, 8723, 8729, 8763, 8769, 8785, 8787, 8789, 8905, 8943, 8949, 8961, 8965, 8985, 8987, 9058, 9070, 9074, 9214, 9218, 9238, 9254, 9258, 9290, 9294, 9410, 9418, 9434, 9454, 9470, 9474, 9478, 9494, 9498, 9638, 9654, 9658, 9670, 9674, 9678, 9694, 9698, 9814, 9830, 9854, 9878, 10105, 10127, 10149, 10165, 10329, 10365, 10385, 10387, 10505, 10507, 10509, 10549, 10563, 10569, 10585.

Some larger examples :