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amenable n.  and  Rhonda n.

First numbers that belong to both sets:

1568, 4752, 5265, 5664, 5824, 5832, 12985, 15625, 25284, 35581, 47265, 53176, 55272, 56356, 95232, 118465, 133857, 148653, 161785, 172577, 224256, 226953, 232356, 242352, 254624, 256973, 259333, 272952, 295412, 315288, 316285, 339521, 342225, 365313, 392533, 456841, 513744, 516817, 518668, 521356, 531729, 562696, 563125, 643528, 668185, 671865, 681265, 733125, 749425, 844185, 859341, 885521, 954664, 1119657, 1145896, 1186593, 1292656, 1326265, 1351896, 1387825, 1389513, 1425424, 1451892, 1454516, 1534392, 1543345, 1555224, 1557532, 1583197, 1584117, 1644852, 1755325, 1875592, 2115764, 2128753, 2156517, 2185561, 2217485, 2355676, 2444525, 2517165, 2572844, 2682456, 2721485, 2853729, 2918545, 2944513, 3132853, 3255265, 3257232, 3366153, 3574296, 3643465, 3712365, 3882568, 3942856, 4152336, 4167745, 4194544, 4253665, 4312753, 4525236, 4591812, 4716541, 4768353, 5116384, 5139916, 5142552, 5151328, 5267176, 5288236, 5397437, 5454216, 5523224, 5531169, 5613669, 5674156, 5711616, 5722165, 5826176, 5831252, 5868121, 5929153, 5961544, 6256832, 6325128, 6412952, 6452864, 6521792, 6544728, 6754321, 6925225, 6965416, 7115724, 7116252, 7255381, 7314385, 7335296, 7355649, 7384653, 7614265, 7641517, 7784225, 7825233, 7911584, 7925872, 7952317, 8116537, 8124573, 8161573, 8217185, 8411757, 8511529, 8519924, 8591121, 8631156, 9111657, 9158232, 9213385, 9214557, 9541116, 9892552, 11155928, 11169865, 11175829, 11182752, 11225472, 11439156, 11528125, 11588461, 11731265, 11741752, 11745245, 11755612, 11881745, 11927513, 12191445, 12193568, 12251169, 12287853, 12343752, 12395844, 12463561, 12553456, 12555124, 12615552, 12665157, 12962532, 13132592, 13159832, 13442557, 13518817, 13522585, 13534136, 13545145, 13615741, 13795124, 13828945, 13861581, 13953612, 13955725, 13985257, 14156148, 14156316, 14215745, 14248588, 14312544, 14367592, 14854945, 15148164, 15155721, 15163681, 15164148, 15183128, 15226496, 15261176, 15285772, 15317225, 15332628, 15342817, 15352513, 15421185, 15445144, 15461432, 15542641, 15587712, 15648721, 15652164, 15811444, 15891441, 16119752, 16145437, 16258413, 16384552, 16751821, 16791541, 16945112, 17225156, 17342516, 17413585, 17451616, 17528196, 17758225, 18315153, 18315817, 18328513, 18511416, 19155192, 19795132, 21138165, 21215684, 21437652, 21492548, 21567812, 21643125, 21658176, 21685288, 21727541, 22126357, 22151476, 22155837, 22175637, 22218529, 22416352, 22435172, 22446516, 22465812, 22551924, 22815632, 22827588, 22942153, 23254465, 23524665, 23546413, 23757125, 23766145, 24253125, 24261853, 24312457, 24356848.

Some larger examples :