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balanced n.  and  Lehmer n.

First numbers that belong to both sets:

15, 595, 2701, 2761, 3409, 7957, 8071, 8227, 8245, 8481, 8695, 8827, 9061, 9367, 9997, 10573, 10585, 10795, 11041, 11155, 12403, 12801, 12901, 13333, 13651, 13747, 14089, 14611, 14911, 14989, 15811, 15841, 16405, 16531, 17563, 17611, 18019, 18631, 18721, 18967, 33709, 36391, 36499, 39091, 39817, 39865, 40261, 41395, 41881, 42127, 42217, 42661, 43165, 43621, 47239, 49771, 55969, 132595, 134521, 137311, 138481, 141661, 142681, 144841, 146965, 149443, 151887, 155149, 156877, 159895, 160147, 162401, 167761, 168421, 171205, 172501, 176437, 180851, 181351, 181579, 183061, 186961, 192865, 198535, 198871, 200887, 200911, 204001, 204051, 208273, 208999, 216457, 219781, 221263, 226081, 227461, 228361, 230461, 232531, 234247, 245791, 248005, 248857, 251521, 255109, 257041, 333915, 527101, 546013, 553519, 555667, 558811, 559903, 567511, 568429, 568711, 575719, 583771, 585871, 586531, 594301, 601195, 602671, 609451, 631351, 631747, 633907, 637585, 641641, 644371, 645569, 649741, 656635, 657379, 658357, 663181, 665401, 666061, 667711, 668431, 672487, 675469, 676651, 682201, 692455, 695521, 707851, 709171, 725551, 727597, 729391, 729781, 730891, 731971, 733231, 735523, 736291, 738661, 756937, 763981, 771715, 774817, 778339, 780361, 792485, 800299, 823531, 838201, 842821, 864535, 868981, 880663, 886411, 895363, 917995, 918205, 928201, 930721, 931855, 939301, 946191, 960583, 977281, 1018249, 1018921, 1026241, 2135455, 2143327, 2170345, 2174551, 2182267, 2184091, 2184931, 2188957, 2191591, 2220469, 2221765, 2225671, 2242513, 2243953, 2251549, 2271061, 2271451, 2284621, 2287831, 2296507, 2300881, 2311783, 2313841, 2319511, 2321061, 2328151, 2330839, 2344057, 2347303, 2352421, 2353429, 2375017, 2376511, 2378971, 2380351, 2390371, 2391571, 2395861, 2396527, 2399635, 2406517, 2410591, 2418505, 2423345, 2433151, 2434651, 2439271, 2442799, 2463385, 2475115, 2480689, 2483971, 2496181, 2503501, 2508013, 2511031, 2512441, 2515789, 2528197, 2536741, 2568391, 2569381, 2579011, 2606611, 2632939, 2640631, 2671453, 2680021, 2685571, 2688463, 2698891, 2711911, 2713201, 2725021, 2741323, 2741401, 2790031, 2792131, 2819923, 2827147, 2829001, 2836051, 2839189, 2852011, 2855281, 2861209, 2871571, 2873731, 2877961, 2884223, 2893591, 2912587, 2919511, 2920669.

Some larger examples :