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amenable n.  and  Cunningham n.

First numbers that belong to both sets:

5, 8, 9, 17, 24, 28, 33, 37, 48, 65, 80, 101, 120, 124, 129, 145, 168, 197, 217, 224, 244, 257, 288, 325, 344, 360, 401, 440, 485, 513, 528, 577, 624, 677, 728, 785, 840, 901, 960, 1001, 1025, 1088, 1157, 1224, 1297, 1332, 1368, 1445, 1520, 1601, 1680, 1729, 1765, 1848, 1937, 2024, 2049, 2117, 2188, 2196, 2208, 2305, 2400, 2501, 2600, 2705, 2745, 2808, 2917, 3024, 3124, 3137, 3248, 3365, 3376, 3480, 3601, 3720, 3845, 3968, 4097, 4224, 4357, 4488, 4625, 4760, 4901, 4912, 5040, 5185, 5328, 5477, 5624, 5777, 5833, 5928, 6085, 6240, 6401, 6560, 6725, 6860, 6888, 7057, 7224, 7397, 7568, 7745, 7777, 7920, 8001, 8101, 8193, 8280, 8465, 8648, 8837, 9024, 9217, 9260, 9408, 9605, 9800, 10001, 10200, 10405, 10608, 10649, 10817, 11024, 11237, 11448, 11665, 11880, 12101, 12168, 12320, 12545, 12768, 12997, 13224, 13457, 13688, 13825, 13925, 14160, 14401, 14640, 14885, 15128, 15377, 15624, 15877, 16128, 16385, 16640, 16808, 16901, 17160, 17425, 17577, 17688, 17957, 18224, 18497, 18768, 19045, 19320, 19601, 19684, 19880, 20165, 20448, 20737, 21024, 21317, 21608, 21905, 21953, 22200, 22501, 22800, 23105, 23408, 23717, 24024, 24337, 24388, 24648, 24965, 25280, 25601, 25920, 26245, 26568, 26897, 27001, 27224, 27557, 27888, 28225, 28560, 28901, 29240, 29585, 29792, 29928, 30277, 30624, 30977, 31328, 31685, 32040, 32401, 32760, 32769, 33125, 33488, 33857, 34224, 34597, 34968, 35345, 35720, 35936, 36101, 36480, 36865, 37248, 37637, 38024, 38417, 38808, 39205, 39305, 39600, 40001, 40400, 40805, 41208, 41617, 42024, 42437, 42848, 42876, 43265, 43680, 44101, 44520, 44945, 45368, 45797, 46224, 46657, 47088, 47525, 47960, 48401, 48840, 49285, 49728, 50177, 50624, 50652, 51077, 51528, 51985, 52440, 52901, 53360, 53825, 54288, 54757, 54873, 55224, 55697, 56168, 56645, 57120, 57601.

Some larger examples :