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nonagonal n.  and  unprimeable n.

First numbers that belong to both sets:

204, 325, 1350, 1794, 2484, 3286, 3504, 7614, 13734, 16014, 17964, 22200, 26274, 32016, 39804, 46000, 52644, 57024, 58825, 59736, 63450, 68250, 71214, 73225, 76294, 78375, 88086, 93726, 97194, 100725, 103114, 116754, 125875, 145146, 146575, 153825, 156774, 161250, 175056, 179784, 181374, 187804, 192700, 194346, 214644, 218125, 221634, 226950, 241434, 243276, 248844, 250714, 254475, 258264, 271746, 295656, 312156, 320574, 322696, 324825, 339924, 357600, 373434, 375724, 384954, 391950, 410914, 413316, 422994, 430326, 442686, 450186, 470494, 473064, 478225, 480816, 483414, 501796, 512454, 515136, 523224, 531375, 545100, 547866, 556206, 567424, 570246, 573075, 578754, 581604, 587325, 590196, 613416, 616350, 628156, 637084, 640074, 652104, 676500, 685764, 698214, 726636, 736236, 739450, 752376, 762144, 765414, 788500, 805200, 815304, 832284, 839125, 845994, 859816, 873750, 884274, 887796, 901954, 916224, 930606, 956044, 959706, 970734, 974424, 1004196, 1045864, 1049694, 1057375, 1123794, 1155750, 1171896, 1192236, 1208634, 1221006, 1225144, 1237600, 1258500, 1279575, 1309374, 1339516, 1343850, 1361256, 1365625, 1374384, 1396404, 1409700, 1414146, 1463514, 1468044, 1486234, 1499950, 1555444, 1560114, 1578864, 1593000, 1616700, 1631004, 1635786, 1640575, 1674294, 1727974, 1747704, 1767546, 1772524, 1807566, 1812600, 1827744, 1832806, 1853124, 1863325, 1868436, 1873554, 1888950, 1930314, 1940725, 1951164, 1977384, 1993200, 1998486, 2014386, 2057094, 2062464, 2073225, 2084014, 2105676, 2121996, 2127450, 2165824, 2171334, 2182375, 2238000, 2254824, 2260446, 2277354, 2283004, 2299996, 2305674, 2328456, 2368594, 2374356, 2391684, 2397474, 2409075, 2444046, 2461626, 2467500, 2508814, 2514744, 2526625, 2532576, 2538534, 2580436, 2586450, 2604534, 2616625, 2634814, 2646975, 2659164, 2677500, 2732886, 2757684, 2807616, 2832750, 2851674, 2864325, 2877004, 2883354, 2908824, 2979444, 3011824, 3037854, 3063996, 3083676, 3136464, 3143094, 3163026, 3189700, 3243384, 3270394, 3277164, 3358950, 3407124, 3434806, 3441744, 3462600, 3490506, 3497500, 3532575, 3546654, 3553704, 3567825, 3631716, 3660294, 3710575, 3717786, 3725004, 3746700, 3812166, 3819475, 3834114, 3841444, 3870834, 3922536, 3952234, 3982044, 4004475, 4011966, 4049526, 4109986, 4132774, 4140384, 4170894, 4193850, 4255374, 4263096, 4325124, 4348500, 4379766, 4411144, 4419006.

Some larger examples :