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happy n.  and  pseudoperfect n.

First numbers that belong to both sets:

28, 100, 176, 192, 208, 280, 320, 368, 392, 440, 464, 490, 496, 608, 644, 680, 700, 736, 748, 784, 820, 860, 888, 910, 912, 940, 1000, 1088, 1092, 1122, 1128, 1148, 1152, 1158, 1182, 1184, 1188, 1212, 1218, 1288, 1290, 1300, 1330, 1332, 1472, 1484, 1512, 1518, 1572, 1575, 1578, 1752, 1758, 1760, 1812, 1818, 1880, 1888, 1900, 1902, 1920, 1976, 1992, 2030, 2080, 2112, 2118, 2190, 2212, 2260, 2300, 2360, 2448, 2478, 2484, 2548, 2568, 2574, 2584, 2586, 2620, 2658, 2748, 2752, 2754, 2784, 2800, 2844, 2856, 2874, 2910, 3010, 3020, 3100, 3132, 3190, 3200, 3260, 3290, 3312, 3328, 3332, 3380, 3392, 3456, 3465, 3536, 3546, 3560, 3564, 3608, 3620, 3654, 3680, 3760, 3798, 3860, 3920, 3968, 3978, 4004, 4040, 4144, 4172, 4248, 4278, 4284, 4356, 4400, 4428, 4460, 4482, 4494, 4536, 4554, 4572, 4640, 4690, 4712, 4725, 4728, 4752, 4780, 4782, 4788, 4824, 4842, 4872, 4878, 4888, 4900, 4944, 4960, 5056, 5112, 5118, 5172, 5178, 5248, 5268, 5274, 5286, 5336, 5346, 5360, 5364, 5436, 5454, 5472, 5544, 5560, 5572, 5628, 5634, 5660, 5682, 5712, 5718, 5724, 5742, 5824, 5826, 5862, 5994, 6032, 6080, 6136, 6220, 6230, 6258, 6320, 6354, 6370, 6380, 6392, 6435, 6440, 6528, 6534, 6560, 6582, 6650, 6656, 6798, 6800, 6825, 6852, 6940, 6978, 7000, 7084, 7144, 7152, 7158, 7160, 7196, 7245, 7248, 7252, 7254, 7284, 7336, 7360, 7398, 7425, 7428, 7452, 7480, 7482, 7488, 7512, 7518, 7524, 7542, 7552, 7630, 7698, 7744, 7788, 7824, 7840, 7842, 7848, 7878, 7884, 7896, 7900, 7938, 7968, 7986, 8020, 8036, 8060, 8088, 8112, 8118, 8128, 8180, 8200, 8244, 8256, 8274, 8330, 8360, 8424, 8442, 8470, 8472, 8478, 8512, 8526, 8562, 8600, 8652, 8704, 8724, 8740, 8742, 8748, 8778.

Some larger examples :