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plaindrome  and  pseudoperfect n.

First numbers that belong to both sets:

6, 12, 18, 24, 28, 36, 48, 56, 66, 78, 88, 112, 114, 126, 138, 144, 156, 168, 222, 224, 228, 234, 246, 258, 288, 336, 348, 366, 368, 378, 444, 448, 456, 468, 558, 588, 666, 678, 888, 1116, 1122, 1128, 1134, 1144, 1146, 1148, 1158, 1188, 1224, 1236, 1248, 1266, 1278, 1288, 1338, 1344, 1356, 1368, 1446, 1456, 1458, 1488, 1566, 1568, 1578, 1668, 1788, 1888, 2226, 2238, 2244, 2256, 2268, 2288, 2334, 2346, 2358, 2368, 2388, 2448, 2466, 2478, 2556, 2568, 2688, 2778, 3336, 3344, 3348, 3366, 3378, 3388, 3444, 3456, 3468, 3556, 3558, 3588, 3666, 3668, 3678, 3888, 4446, 4458, 4488, 4566, 4578, 4668, 4788, 4888, 5556, 5568, 5688, 5778, 5888, 6666, 6678, 6688, 6888, 7788, 7888, 8888, 11112, 11116, 11118, 11124, 11128, 11136, 11144, 11148, 11166, 11178, 11226, 11228, 11238, 11244, 11248, 11256, 11268, 11288, 11334, 11336, 11346, 11358, 11368, 11388, 11448, 11466, 11478, 11556, 11568, 11688, 11778, 11788, 12222, 12228, 12234, 12236, 12246, 12258, 12288, 12336, 12348, 12366, 12378, 12444, 12456, 12468, 12488, 12558, 12588, 12666, 12678, 12688, 12888, 13338, 13344, 13356, 13368, 13446, 13456, 13458, 13468, 13488, 13566, 13568, 13578, 13668, 13788, 13888, 14448, 14456, 14466, 14478, 14556, 14568, 14588, 14688, 14778, 15558, 15568, 15588, 15666, 15678, 15888, 16668, 16688, 16788, 17778, 17888, 18888, 22224, 22236, 22248, 22256, 22266, 22278, 22288, 22338, 22344, 22356, 22368, 22446, 22448, 22456, 22458, 22488, 22566, 22568, 22578, 22668, 22788, 23334, 23346, 23358, 23388, 23448, 23466, 23478, 23556, 23568, 23688, 23778, 24444, 24448, 24456, 24468, 24556, 24558, 24588, 24666, 24668, 24678, 24888, 25566, 25568, 25578, 25668, 25688, 25788, 26688, 26778, 27888, 33336, 33345, 33348, 33366, 33378, 33444, 33456, 33468, 33488, 33558, 33588, 33666, 33678, 33888, 34446, 34458, 34468.

Some larger examples :