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Harshad n.  and  hexagonal n.

First numbers that belong to both sets:

1, 6, 45, 120, 153, 190, 378, 630, 780, 1035, 1128, 1431, 1540, 1770, 2016, 2556, 2850, 3160, 3321, 3486, 4005, 4560, 4950, 5565, 5778, 7140, 8911, 9180, 10011, 10296, 11175, 11476, 12720, 13041, 14706, 15400, 16110, 17205, 17955, 21528, 21945, 23220, 24090, 24976, 28680, 29646, 30628, 31626, 32640, 35245, 39060, 41328, 51040, 51681, 52326, 56280, 61776, 63903, 64620, 65341, 69006, 70500, 72010, 73536, 76636, 78210, 79800, 89676, 93096, 100128, 101025, 103740, 105570, 106491, 113050, 114003, 117855, 121771, 122760, 123753, 139128, 141246, 145530, 161028, 164451, 165600, 182106, 201930, 204480, 209628, 220116, 224115, 225456, 228150, 236328, 244650, 253116, 254541, 260281, 264628, 266085, 270480, 285390, 300700, 303810, 306936, 313236, 316410, 321201, 327645, 332520, 334153, 340725, 349030, 352380, 359128, 371091, 372816, 383250, 386760, 404550, 430128, 441330, 460320, 471906, 475800, 487578, 499500, 519690, 525825, 536130, 554931, 565516, 580503, 582660, 595686, 600060, 613278, 622170, 626640, 628881, 653796, 658378, 662976, 667590, 672220, 674541, 705078, 724206, 738720, 741153, 748476, 768180, 770661, 805815, 810901, 828828, 839160, 878475, 910575, 913276, 915981, 924120, 937765, 951510, 979300, 987715, 990528, 1001820, 1010331, 1016025, 1024596, 1030330, 1036080, 1059240, 1112286, 1124250, 1127251, 1130256, 1133265, 1142316, 1154440, 1185030, 1203576, 1216020, 1225395, 1228528, 1241100, 1250571, 1269621, 1272810, 1288815, 1304920, 1308153, 1311390, 1321125, 1334161, 1357128, 1370340, 1400301, 1410360, 1423828, 1437360, 1447551, 1492128, 1505980, 1540890, 1544403, 1619100, 1637145, 1684530, 1728870, 1736316, 1785105, 1804050, 1811656, 1838403, 1849926, 1876953, 1911990, 1919820, 1943406, 1951300, 1991010, 1995003, 2015028, 2019045, 2031120, 2047276, 2104326, 2112540, 2145556, 2162160, 2178828, 2183005, 2203950, 2216565, 2229216, 2250381, 2263128, 2275911, 2280180, 2288730, 2331720, 2410110, 2471976, 2507680, 2543640, 2598060, 2634660, 2680770, 2760075, 2774190, 2783620, 2821500, 2831010, 2859636, 2917320, 2951235, 2975580, 2995128, 3019653, 3034416, 3064050, 3069003, 3123750, 3143778, 3153816, 3194128, 3219453, 3275520, 3357936, 3420420, 3430890, 3483480, 3557778, 3573801, 3579150, 3611328, 3632860.

Some larger examples :