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amenable n.  and  magic constant

First numbers that belong to both sets:

1, 5, 65, 260, 369, 505, 1105, 2056, 2465, 2925, 4641, 6924, 7825, 8801, 12209, 16400, 17985, 19669, 25345, 32020, 34481, 37065, 45585, 55320, 58849, 62525, 74465, 87836, 92625, 97585, 113521, 131104, 137345, 143781, 164289, 186660, 194545, 202649, 228305, 256040, 265761, 275725, 307105, 340780, 352529, 364545, 402225, 442416, 456385, 470645, 515201, 562484, 578865, 595561, 647569, 702520, 721505, 740829, 800865, 864060, 885841, 907985, 976625, 1048640, 1073409, 1098565, 1176385, 1257796, 1285745, 1314105, 1401681, 1493064, 1524385, 1556141, 1654049, 1755980, 1790865, 1826209, 1935025, 2048080, 2086721, 2125845, 2246145, 2370900, 2413489, 2456585, 2588945, 2725976, 2772705, 2819965, 2964961, 3114844, 3165905, 3217521, 3375729, 3539040, 3594625, 3650789, 3822785, 4000100, 4060401, 4121305, 4307665, 4499560, 4564769, 4630605, 4831905, 5038956, 5109265, 5180225, 5397041, 5619824, 5695425, 5771701, 6004609, 6243700, 6324785, 6406569, 6656145, 6912120, 6998881, 7086365, 7353185, 7626620, 7719249, 7812625, 8097265, 8388736, 8487425, 8586885, 8889921, 9200004, 9304945, 9410681, 9732689, 10061960, 10173345, 10285549, 10627105, 10976140, 11094161, 11213025, 11574705, 11944080, 12068929, 12194645, 12577025, 12967316, 13099185, 13231945, 13635601, 14047384, 14186465, 14326461, 14751969, 15185820, 15332305, 15479729, 15927665, 16384160, 16538241, 16693285, 17164225, 17643940, 17805809, 17968665, 18463185, 18966696, 19136545, 19307405, 19826081, 20353964, 20531985, 20711041, 21254449, 21807280, 21993665, 22181109, 22749825, 23328180, 23523121, 23719145, 24313745, 24918200, 25121889, 25326685, 25947745, 26578876, 26791505, 27005265, 27653361, 28311744, 28533505, 28756421, 29432129, 30118340, 30349425, 30581689, 31285585, 32000200, 32240801, 32482605, 33215265, 33958860, 34209169, 34460705, 35222705, 35995856, 36256065, 36517525, 37309441, 38112724, 38383025, 38654601, 39477009, 40311000, 40591585, 40873469, 41726945, 42592220, 42883281, 43175665, 44060785, 44957920, 45259649, 45562725, 46480065, 47409636, 47722225, 48036185, 48986321, 49948904, 50272545, 50597581, 51581089, 52577260, 52912145, 53248449, 54265905, 55296240, 55642561, 55990325, 57042305, 58107380, 58465329, 58824745, 59911825, 61012216, 61381985, 61753245, 62876001, 64012284, 64394065, 64777361, 65936369, 67109120, 67503105, 67898629, 69094465, 70304260, 70710641, 71118585, 72351825, 73599240, 74018209, 74438765, 75709985, 76995596, 77427345, 77860705, 79170481, 80494864, 80939585, 81385941, 82734849, 84098580, 84556465, 85016009, 86404625, 87808280.

Some larger examples :