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economical n.  and  triangular n.

First numbers that belong to both sets:

1, 3, 10, 15, 21, 105, 1081, 1225, 1431, 1711, 1891, 2485, 2701, 3321, 3403, 4753, 10011, 10585, 10731, 12403, 12561, 13041, 13203, 13861, 15753, 15931, 18721, 29403, 29646, 31125, 31375, 32896, 100576, 104653, 108811, 110215, 114481, 117855, 118341, 120295, 123753, 124251, 124750, 126253, 130816, 131328, 140185, 146611, 153181, 158203, 160461, 166753, 169071, 171991, 180901, 188191, 193753, 195625, 205120, 216811, 218791, 226801, 234955, 235641, 251695, 258121, 266085, 269011, 275653, 281625, 286903, 295296, 327645, 328455, 341551, 344035, 351541, 354061, 364231, 371953, 385003, 392941, 439453, 470935, 471906, 482653, 497503, 524800, 737505, 780625, 1033203, 1034641, 1056331, 1057785, 1062153, 1063611, 1073845, 1091503, 1104841, 1127251, 1145341, 1159003, 1178880, 1180416, 1181953, 1183491, 1269621, 1309771, 1314631, 1316253, 1347261, 1348903, 1353835, 1355481, 1368685, 1373653, 1375311, 1408681, 1413721, 1447551, 1456071, 1468041, 1469755, 1537381, 1551441, 1553203, 1558495, 1574425, 1644391, 1658931, 1660753, 1690041, 1710325, 1725153, 1755001, 1756875, 1758750, 1771903, 1792671, 1794565, 1817371, 1848003, 1869211, 1884711, 1886653, 1933561, 1963171, 1965153, 1987021, 2096128, 2098176, 2118711, 2390391, 2392578, 2414503, 2881200, 2883601, 2951235, 3126250, 3275520, 3541791, 3544453, 3946645, 4252986, 4717056, 4720128, 4881250, 4884375, 5649841, 5788503, 5884165, 6060421, 6420736, 6641190, 6644835, 6835753, 6924781, 9563751, 9568125, 9757153, 10037440, 10041921, 10046403, 10064341, 10077805, 10131751, 10154271, 10185841, 10280845, 10335331, 10389961, 10403641, 10426461, 10444735, 10499653, 10554715, 10642191, 10660653, 10679131, 10753203, 10757841, 10916128, 10944181, 11000395, 11056753, 11127403, 11146281, 11151003, 11212480, 11283625, 11297881, 11354995, 11417031, 11431371, 11436153, 11455291, 11469655, 11512801, 11527201, 11532003, 11546415, 11584891, 11686195, 11700703, 11783085, 11812230, 11860885, 11934055, 11992753, 12051595, 12066328, 12071241, 12095821, 12169711, 12189453, 12209211, 12214153, 12273535, 12288403, 12313203, 12347965, 12367851, 12497500, 12512503, 12607731, 12612753, 12668061, 12708361, 12713403, 12814453, 12890503, 12936241, 12951505, 12997351, 13012651, 13017753, 13073941, 13099521, 13104640, 13109760, 13217511, 13238085, 13243231, 13279281, 13408431, 13429153, 13434336, 13569445, 13679065, 13694761, 13715703, 13783875, 13841691, 14010571, 14031753, 14037051, 14164503, 14169826, 14185801, 14201785.

Some larger examples :