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economical n.  and  nonagonal n.

First numbers that belong to both sets:

1, 111, 1216, 1491, 2125, 10071, 11629, 12871, 14176, 16975, 22761, 23329, 28125, 30691, 32689, 48439, 54375, 75264, 106750, 109209, 110449, 114211, 124551, 125875, 129889, 140901, 152361, 158259, 161250, 164269, 195999, 202681, 206064, 218125, 228736, 245125, 267859, 293625, 410914, 564609, 825471, 866769, 978121, 1011709, 1023031, 1057375, 1068949, 1104049, 1115875, 1123794, 1151731, 1163809, 1180011, 1216875, 1229289, 1300825, 1313659, 1317951, 1330869, 1352539, 1365625, 1432000, 1436481, 1440969, 1490799, 1518336, 1527571, 1569475, 1742761, 1757611, 1802539, 1858221, 1925119, 1966875, 2003779, 2025021, 2030349, 2067841, 2116549, 2165824, 2221239, 2249209, 2455759, 2568429, 2598499, 2689759, 2745271, 2770125, 2928000, 2972989, 2992375, 3077109, 3209779, 3229921, 3256875, 3372679, 3624589, 3703371, 4155625, 4340701, 4426875, 4434751, 4498011, 4796416, 4920121, 5163750, 5249125, 5326561, 5465625, 5749129, 5966461, 6076639, 6281250, 6413221, 6556141, 7436529, 7508125, 8844375, 9885961, 10027639, 10086969, 10122651, 10278001, 10290000, 10326039, 10422451, 10604431, 10714375, 10751149, 10763421, 10861849, 11010331, 11047609, 11234944, 11297739, 11348101, 11449161, 11499859, 11512551, 11652625, 11703771, 11961181, 11974125, 12064929, 12077929, 12273769, 12300000, 12497625, 12550591, 12590389, 12710161, 12750211, 12924489, 13072879, 13154176, 13181331, 13509375, 13523131, 13564441, 13647250, 13674909, 13855375, 13911141, 14233969, 14517699, 14818629, 14919625, 15035469, 15268501, 15621409, 15799375, 15829134, 15978349, 16218549, 16278879, 16339321, 16521319, 16734924, 16780875, 16857600, 16888339, 17073361, 17166250, 17197269, 17571681, 17713125, 17760399, 18348625, 19175131, 19306431, 19769509.