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aban n.  and  hexagonal n.

First numbers that belong to both sets:

1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703, 780, 861, 946, 3000025, 49000050, 75000628, 84000241, 163000540, 235000360, 364000671, 366000040, 398000791, 428000653, 437000266, 458000245, 565000920, 571000321, 792000100, 818000128, 935000146, 973000441, 1098000091, 1167000516, 1210000221, 1474000660, 1479000078, 1553000046, 1590000636, 1597000870, 1614000520, 1663000956, 1753000866, 1841000860, 1969000881, 2159000616, 2169000316, 2317000701, 2527000686, 2952000703, 3199000078, 3203000703, 3550000191, 3576000165, 3606000426, 3645000271, 4023000150, 4141000515, 4172000185, 4284000766, 4289000653, 4312000545, 4545000811, 4566000141, 5071000278, 5146000525, 5377000551, 5490000505, 5978000496, 5985000528, 6119000625, 6160000510, 6186000835, 7857000690, 8235000280, 9030000078, 10002000330, 10183000695, 10225000506, 10620000930, 10729000855, 10858000566, 11593000315, 12299000703, 12699000028, 12736000200, 12798000078, 12806000703, 13701000880, 14078000503, 14548000600, 14773000105, 14867000830, 15239000910, 15386000490, 15533000640, 15736000906, 15817000870, 16174000440, 16495000896, 16706000655, 16992000378, 17208000370, 17318000778, 17397000246, 17734000285, 18658000551, 18752000970, 18952000705, 19655000778, 20412000225, 20843000706, 20996000740, 21333000403, 21448000941, 22073000995, 22936000753, 22981000078, 23217000355, 24741000235, 24880000915, 25476000675, 27247000080, 27311000041, 27465000006, 27642000375, 27722000845, 28046000703, 28156000951, 28797000078, 28809000703, 29387000961, 29469000606, 29804000878, 30031000350, 30536000628, 30876000750, 30971000521, 31125000250, 32015000361, 32297000781, 32544000126, 33204000753, 33318000730, 34822000851, 34971000345, 36161000128, 38200000215, 39257000706, 39386000116, 39994000431, 40037000851, 40241000971, 40990000681, 41435000256, 41839000356, 42116000878, 42170000491, 42612000346, 42881000526, 43332000078, 43582000230, 43712000650, 44061000231, 44080000903, 44325000411, 45165000975, 45968000445, 47491000336, 49151000746, 50193000703, 51109000470, 51196000078, 51212000703, 51809000253, 52425000915, 52761000061, 52865000541, 54146000503, 55667000278, 55850000220, 55957000380, 56176000455, 56509000471, 57337000930, 57908000403, 59020000665, 60162000003, 60611000365, 61999000911, 62638000596, 64561000780, 64584000300, 65060000281, 65273000016, 65745000420, 68758000696, 69139000153, 69264000721, 70083000078, 70827000265, 72057000876, 75002000556, 76679000245, 76726000585, 78740000703, 79983000903, 79987000528, 79991000253, 79995000078, 79999000003, 80003000028, 80007000153, 80011000378, 80015000703, 80507000745, 80621000475, 81077000586, 84974000628, 86621000976, 87193000810, 88473000925, 88542000891, 88992000021, 89587000405, 90382000866, 91543000555, 92131000653, 92210000961, 96997000128, 97810000905, 101149000200, 101712000825, 102482000085, 103234000078, 103924000656, 106622000436, 108076000581, 108602000326, 109176000121, 110368000225, 113687000703, 113853000705, 113937000841, 114841000126, 115194000078, 115218000703, 116263000945, 117304000066, 117653000986, 118159000875, 119707000350, 120665000631, 120837000606, 120896000226, 121336000653, 123385000420, 124646000986, 125354000278, 125792000571, 126063000381, 126462000070, 127383000396, 129748000528, 129960000576, 131535000156, 132841000846, 133264000716, 142785000078, 142986000466, 147585000160, 147785000616.

Some larger examples :