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Harshad n.  and  Hogben n.

First numbers that belong to both sets:

1, 3, 7, 21, 111, 133, 2353, 4557, 7833, 10101, 11991, 13111, 14521, 14763, 15751, 20881, 22953, 26733, 34411, 37443, 39007, 40201, 53131, 55461, 61257, 72093, 77007, 83811, 89103, 96411, 115941, 124257, 130683, 139503, 141001, 146307, 150157, 155631, 162813, 166873, 172641, 190533, 209307, 217623, 222313, 249501, 270921, 280371, 291061, 293223, 311923, 316407, 326613, 340473, 351057, 365421, 391251, 401323, 402591, 432307, 472657, 474033, 479557, 503391, 504811, 516243, 532171, 533631, 610743, 644007, 663411, 691393, 709807, 713181, 770007, 807303, 810901, 862113, 901551, 945757, 973183, 1001001, 1009021, 1011031, 1021111, 1025157, 1049601, 1068123, 1093071, 1101451, 1111971, 1137423, 1148113, 1156701, 1213303, 1257763, 1323651, 1344441, 1370071, 1372413, 1422057, 1443603, 1598961, 1652511, 2026353, 2052057, 2112663, 2174151, 2230543, 2236521, 2324101, 2336313, 2385481, 2400951, 2510641, 2561601, 2600157, 2684683, 2807301, 2867943, 2987713, 3015433, 3022383, 3170181, 3245403, 3299673, 3321507, 3555111, 3711403, 3750033, 3835723, 3886813, 3890757, 4026043, 4046133, 4082421, 4102651, 4131057, 4179981, 4249783, 4303551, 4320163, 4336807, 4391121, 4698057, 4750221, 4842201, 4868643, 4957303, 5060251, 5123433, 5260143, 5315331, 5398653, 5412603, 5557807, 5671543, 5810511, 5926791, 6118203, 6222531, 6277531, 6332773, 6373101, 6945861, 6956407, 6972241, 7025151, 7078261, 7201173, 7238791, 7314321, 7439257, 7576257, 7753441, 7792473, 7814821, 7977801, 8011731, 8131053, 8199633, 8303043, 8459373, 8523481, 8640661, 8823871, 8883381, 8919183, 9366661, 9385033, 9452551, 9594507, 9837633, 9875307, 10001407, 10026723, 10083801, 10160157, 10217613, 10262413, 10352307, 10358743, 10624341, 10702713, 11039007, 11052301, 11098893, 11245963, 11400753, 11461611, 11543007, 11604243, 11830161, 12037431, 12120843, 12330633, 12415053, 12478557, 13014057, 13166013, 13195057, 13224133, 13231407, 13849563, 13886803, 13894257, 14006307, 14254401, 14261953, 14322441, 14413413, 14642103, 15128211, 15221703, 15292011, 15338973, 15464557, 15645981, 15693483, 15756931, 16052043, 16124241, 16285261, 16447081, 16479541, 16585257, 16953807, 17061031, 17152023, 17276493, 17468221, 17560291, 17602221, 17930991, 18194491, 18314121, 18545943, 18614911, 18883371, 18935553, 18970381, 19040133, 19276491, 19294057, 19567353, 19913907, 20003257, 20030101, 20048007, 20155611, 20200531, 20236503, 20344611, 20616141, 21109431, 21192213, 21284383, 21302841, 21386001, 21487861.

Some larger examples :