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happy n.  and  unprimeable n.

First numbers that belong to both sets:

208, 320, 326, 536, 622, 1076, 1148, 1330, 1332, 1335, 1418, 1670, 1760, 1796, 1852, 1920, 2185, 2188, 2190, 2360, 2484, 2485, 2518, 2568, 2582, 2584, 2586, 2825, 3056, 3092, 3238, 3260, 3506, 3560, 3564, 3664, 3680, 3896, 3970, 3978, 4064, 4144, 4148, 4184, 4414, 4418, 4474, 4536, 4552, 4554, 4555, 4558, 4572, 4712, 4714, 4715, 4718, 4744, 4774, 4775, 4824, 4825, 4842, 4852, 4855, 5065, 5066, 5128, 5218, 5242, 5245, 5248, 5254, 5255, 5360, 5364, 5422, 5425, 5428, 5452, 5454, 5455, 5458, 5542, 5544, 5545, 5548, 5605, 5606, 5722, 5724, 5725, 5752, 5965, 5978, 5994, 6230, 6404, 6435, 6436, 6505, 6506, 6530, 6534, 6932, 6938, 7084, 7090, 7142, 7144, 7145, 7148, 7160, 7408, 7425, 7428, 7444, 7610, 7804, 7895, 7896, 7985, 7986, 8020, 8074, 8152, 8180, 8182, 8188, 8252, 8254, 8256, 8306, 8330, 8332, 8396, 8452, 8455, 8470, 8472, 8478, 8488, 8554, 8555, 8630, 8652, 8724, 8795, 8796, 8874, 9032, 9070, 9210, 9302, 9362, 9368, 9386, 9444, 9565, 9578, 9594, 9655, 9700, 9758, 9890, 9892, 9896, 9912, 9915, 9954, 9980, 9982, 9986, 10088, 10122, 10125, 10128, 10290, 10418, 10444, 10448, 10572, 10574, 10575, 10578, 10670, 10742, 10744, 10745, 10748, 10760, 10808, 10812, 10814, 10815, 10818, 10825, 10828, 10874, 10875, 10920, 11012, 11014, 11015, 11102, 11104, 11105, 11120, 11124, 11125, 11186, 11202, 11205, 11208, 11220, 11342, 11348, 11408, 11455, 11456, 11538, 11564, 11644, 11645, 11726, 11762, 11764, 11840, 11842, 11850, 11914, 11915, 12022, 12058, 12085, 12088, 12120, 12132, 12134, 12138, 12176, 12180, 12184, 12292, 12312, 12314, 12318, 12330, 12358, 12366, 12382, 12384, 12385, 12465, 12622, 12625, 12628, 12770, 12776, 12778, 12810, 12814, 12832, 12834, 12835, 12862, 12865, 12990, 12995, 12996, 13114, 13230, 13274, 13282, 13284, 13285, 13350, 13370, 13582, 13606.

Some larger examples :