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happy n.  and  semiprime

First numbers that belong to both sets:

10, 49, 82, 86, 91, 94, 129, 133, 203, 219, 226, 262, 291, 301, 302, 319, 326, 329, 362, 365, 386, 391, 446, 469, 478, 565, 566, 622, 623, 635, 649, 655, 671, 694, 763, 793, 802, 818, 899, 901, 913, 921, 923, 973, 989, 998, 1003, 1067, 1114, 1115, 1121, 1141, 1177, 1211, 1247, 1257, 1285, 1299, 1333, 1337, 1339, 1366, 1393, 1411, 1418, 1457, 1478, 1527, 1574, 1679, 1706, 1717, 1727, 1745, 1754, 1769, 1814, 1821, 1841, 1851, 1857, 1874, 1882, 1903, 1929, 1959, 1967, 2019, 2026, 2062, 2122, 2147, 2157, 2174, 2177, 2181, 2199, 2206, 2245, 2257, 2258, 2285, 2306, 2369, 2455, 2458, 2471, 2487, 2517, 2518, 2545, 2554, 2571, 2581, 2582, 2602, 2603, 2771, 2811, 2815, 2818, 2845, 2854, 2881, 2899, 2901, 2933, 2991, 2998, 3013, 3029, 3031, 3062, 3065, 3086, 3091, 3097, 3103, 3133, 3139, 3153, 3166, 3173, 3193, 3233, 3238, 3239, 3269, 3293, 3317, 3338, 3351, 3365, 3383, 3466, 3506, 3513, 3563, 3602, 3629, 3635, 3646, 3653, 3661, 3667, 3713, 3763, 3869, 3901, 3902, 3977, 3986, 4009, 4069, 4078, 4087, 4174, 4178, 4181, 4187, 4222, 4258, 4285, 4287, 4406, 4414, 4417, 4449, 4471, 4474, 4555, 4571, 4577, 4609, 4633, 4714, 4741, 4747, 4757, 4781, 4811, 4827, 4841, 4855, 5063, 5065, 5111, 5127, 5182, 5199, 5218, 5242, 5245, 5255, 5257, 5331, 5353, 5363, 5422, 5455, 5458, 5482, 5485, 5506, 5533, 5545, 5554, 5585, 5603, 5606, 5633, 5666, 5714, 5721, 5722, 5747, 5774, 5789, 5799, 5854, 5855, 5919, 5965, 5979, 5991, 5997, 6017, 6022, 6023, 6038, 6049, 6065, 6071, 6107, 6166, 6179, 6239, 6334, 6433, 6463, 6503, 6505, 6506, 6533, 6559, 6595, 6605, 6613, 6631, 6839, 6879, 6893, 6938, 6989, 6998, 7009, 7061, 7063, 7093, 7117.

Some larger examples :