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esthetic n.  and  Harshad n.

First numbers that belong to both sets:

10, 12, 21, 45, 54, 210, 234, 432, 1010, 1012, 1212, 1232, 3210, 3432, 3456, 5432, 5454, 7656, 10101, 12123, 12321, 12345, 21012, 21210, 23232, 23454, 32121, 34545, 43210, 43212, 43232, 43434, 45432, 45456, 45656, 54567, 56565, 76545, 87876, 98787, 101010, 101210, 101232, 121010, 121212, 123210, 210123, 212121, 232101, 321012, 321210, 343434, 345654, 434343, 434565, 454545, 456543, 543210, 543456, 545454, 565434, 654345, 654565, 676767, 676787, 767676, 2101010, 2101212, 2121012, 2121210, 2123212, 2321010, 2343210, 2343212, 2343232, 2343432, 4323210, 4323456, 4345434, 4345456, 4565678, 6543234, 6765656, 10101012, 10101210, 10121010, 10121232, 10123210, 10123212, 10123232, 10123434, 12101010, 12101232, 12121210, 12121212, 12123232, 12123234, 12123432, 12123456, 12321010, 12321012, 12321232, 12321234, 12323232, 12343212, 12345432, 32101210, 32101212, 32121010, 32121012, 32121232, 32121234, 32123210, 32123232, 32321232, 32323212, 32343210, 32343432, 32345676, 34321212, 34323210, 34323432, 34343232, 34343456, 34345656, 34543432, 34543456, 34545456, 34567676, 54321012, 54321210, 54323232, 54323456, 54345456, 54543456, 54565454, 54565676, 54567656, 56545676, 56565432, 56765456, 56765656, 56767878, 76543232, 76545432, 76545656, 76565454, 76565456, 76787676, 78765456, 98765676, 98767678, 98787654, 101010123, 101012121, 101210121, 101212101, 101234343, 121010121, 121012101, 121210101, 121212343, 121232321, 121234323, 123234321, 123234345, 123456567, 210101010, 210101232, 210101234, 210121210, 210121212, 210123232, 210123234, 210123432, 210123456, 212101210, 212101212, 212101232, 212121010, 212121012, 212121232, 212121234, 212123232, 212321232, 212323212, 212343210, 212343432, 212345432, 212345676, 232101010, 232101012, 232101212, 232101232, 232101234, 232121232, 232123212, 232321212, 232323210, 232323432, 232343232, 232343456, 232345656, 234321012, 234321210, 234323232, 234323456, 234345456, 234345678, 234543232, 234543456, 321010101, 323212323, 323232101, 323434323, 343232343, 343234343, 345432101, 345456765, 345654543, 345656565, 345676545, 345678765, 432101012, 432101232, 432121212, 432123210, 432123432, 432321012, 432321210, 432323232, 432323456, 432343456, 432345456, 434321010, 434321232, 434343456, 434545432, 434565432, 454323456, 454543232, 454545432, 454565454, 456543210, 456543432, 456565456, 456567678, 456765456, 543212321, 543234545, 543432321, 543456765, 545456565, 545654343, 545654565, 545656545, 545676789, 565454565, 565456545, 565654323, 565654545, 567654321, 567654345, 567656765, 567656787, 567878787, 654343232, 654345432, 654345676, 654543210, 654543432, 654543456, 656543232, 656543454, 656565456, 656565676, 656767656, 656787656, 676543212, 676543434.

Some larger examples :