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happy n.  and  nonagonal n.

First numbers that belong to both sets:

1, 2484, 4959, 5781, 6364, 8281, 8625, 8976, 11229, 13299, 14176, 14625, 15081, 16975, 20026, 21099, 22761, 25075, 26274, 27501, 31350, 34056, 40554, 41311, 42075, 44409, 52644, 57024, 61579, 63450, 65349, 68250, 72216, 73225, 74241, 75264, 82621, 92584, 100725, 103114, 109209, 127206, 131241, 156774, 168850, 202681, 221634, 223399, 262081, 283575, 320574, 326961, 346500, 371151, 389611, 420564, 445179, 452700, 457749, 467931, 488631, 496509, 501796, 504450, 515136, 547866, 550639, 570246, 587325, 652104, 685764, 701344, 723450, 778564, 795159, 808561, 852891, 866769, 877251, 894861, 905511, 909075, 934219, 937839, 967051, 981825, 1011709, 1034416, 1053531, 1061226, 1080586, 1092286, 1163809, 1180011, 1208634, 1229289, 1254306, 1266909, 1300825, 1317951, 1335189, 1481676, 1509129, 1654984, 1659801, 1674294, 1703469, 1787500, 1842951, 1868436, 1940725, 1972126, 1993200, 2003779, 2014386, 2046375, 2078616, 2121996, 2154825, 2198989, 2210100, 2243601, 2249209, 2254824, 2271711, 2283004, 2299996, 2305674, 2311359, 2432361, 2438200, 2461626, 2467500, 2544499, 2562436, 2568429, 2702046, 2720529, 2732886, 2776356, 2801350, 2807616, 2820169, 2870661, 2979444, 2985906, 2998851, 3005334, 3083676, 3110014, 3129841, 3196386, 3250126, 3311119, 3338409, 3469566, 3490506, 3553704, 3574896, 3725004, 3768459, 3790281, 3863476, 3982044, 4094829, 4125171, 4340701, 4348500, 4403289, 4585725, 4617831, 4625875, 4641984, 4788225, 4837476, 4886979, 4903536, 4911825, 4961706, 4986741, 5189289, 5214891, 5292075, 5465625, 5527029, 5571099, 5794074, 5848239, 6012246, 6049000, 6067419, 6104341, 6206454, 6271876, 6290631, 6356494, 6394284, 6422700, 6479721, 6498784, 6546564, 6584914, 6720021, 6729724, 6778344, 6984459, 7004250, 7033989, 7043916, 7093656, 7113601, 7254000, 7274169, 7344981, 7365276, 7395771, 7487634, 7580064, 7621326, 7839789, 7871250, 7923825, 7997724, 8114544, 8178621, 8221479, 8329114, 8350725, 8459200, 8491879, 8557426, 8700309, 8766654, 8833251, 8855506, 9057061, 9068325, 9090874, 9102159, 9124750, 9136056, 9238125, 9249501, 9340761, 9375099, 9409500, 9605629, 9686976, 9768666, 9850699, 9897729, 9980301.