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hexagonal n.  and  Smith n.

First numbers that belong to both sets:

378, 861, 2556, 10296, 27261, 46056, 72771, 92235, 120786, 132870, 157641, 345696, 386760, 424581, 529935, 683865, 778128, 897130, 959805, 993345, 1082656, 1234806, 1457778, 1495585, 1597578, 1633528, 1680861, 1792671, 1876953, 1931595, 1983036, 2087946, 2137278, 2396955, 2458653, 2859636, 3296028, 3378700, 3383901, 3451878, 3467661, 3579150, 3654456, 3757911, 3935415, 4444671, 4710915, 6725278, 6984453, 7051890, 7486515, 8158780, 8280415, 8485140, 8501626, 9651421, 9677800, 10158778, 10330785, 10986328, 11556028, 12149985, 12159846, 12328095, 12527515, 12597690, 13155885, 13559028, 13590291, 13736661, 13873278, 13968255, 14063556, 14761461, 14804961, 14881240, 15598905, 17190316, 17841351, 18945090, 19006695, 19043706, 19378425, 19892278, 19942770, 19955403, 20259795, 21264981, 22656546, 23252790, 23334696, 25988445, 26393745, 26553828, 26846128, 27762426, 27807153, 29196261, 29518086, 30556653, 32477770, 32768560, 33386706, 33648706, 33812976, 35141536, 35866215, 36359128, 36495696, 37493470, 37858051, 38574936, 41527941, 42168336, 42943278, 43407903, 44816778, 45481953, 47799753, 47917155, 48348861, 48447246, 49059465, 49895055, 49995000, 50095045, 50275378, 50556540, 51485878, 51689028, 52608153, 53908536, 54575128, 56068755, 56705925, 57154086, 57239650, 57646953, 57969528, 58141936, 58249821, 58530790, 61266915, 65088345, 65111166, 65316735, 65728845, 67343815, 67576125, 68579616, 69732145, 71874055, 72764016, 73489626, 74658090, 74706976, 75638850, 77121990, 77569740, 78218778, 80384860, 83844775, 84831825, 85955716, 87509835, 87854140, 87960216, 90148878, 90579070, 90605991, 92337255, 93017980, 93454956, 94331980, 94606890, 95627535, 95793561, 96764916, 97294275, 98919145, 99059850, 99144321, 99680140, 99906180.