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amenable n.  and  Jordan-Polya n.

First numbers that belong to both sets:

1, 8, 12, 16, 24, 32, 36, 48, 64, 72, 96, 120, 128, 144, 192, 216, 240, 256, 288, 384, 432, 480, 512, 576, 720, 768, 864, 960, 1024, 1152, 1296, 1440, 1536, 1728, 1920, 2048, 2304, 2592, 2880, 3072, 3456, 3840, 4096, 4320, 4608, 5040, 5184, 5760, 6144, 6912, 7680, 7776, 8192, 8640, 9216, 10080, 10368, 11520, 12288, 13824, 14400, 15360, 15552, 16384, 17280, 18432, 20160, 20736, 23040, 24576, 25920, 27648, 28800, 30240, 30720, 31104, 32768, 34560, 36864, 40320, 41472, 46080, 46656, 49152, 51840, 55296, 57600, 60480, 61440, 62208, 65536, 69120, 73728, 80640, 82944, 86400, 92160, 93312, 98304, 103680, 110592, 115200, 120960, 122880, 124416, 131072, 138240, 147456, 155520, 161280, 165888, 172800, 181440, 184320, 186624, 196608, 207360, 221184, 230400, 241920, 245760, 248832, 262144, 276480, 279936, 294912, 311040, 322560, 331776, 345600, 362880, 368640, 373248, 393216, 414720, 442368, 460800, 483840, 491520, 497664, 518400, 524288, 552960, 559872, 589824, 604800, 622080, 645120, 663552, 691200, 725760, 737280, 746496, 786432, 829440, 884736, 921600, 933120, 967680, 983040, 995328, 1036800, 1048576, 1088640, 1105920, 1119744, 1179648, 1209600, 1244160, 1290240, 1327104, 1382400, 1451520, 1474560, 1492992, 1572864, 1658880, 1679616, 1728000, 1769472, 1843200, 1866240, 1935360, 1966080, 1990656, 2073600, 2097152, 2177280, 2211840, 2239488, 2359296, 2419200, 2488320, 2580480, 2654208, 2764800, 2903040, 2949120, 2985984, 3110400, 3145728, 3317760, 3359232, 3456000, 3538944, 3628800, 3686400, 3732480, 3870720, 3932160, 3981312, 4147200, 4194304, 4354560, 4423680, 4478976, 4718592, 4838400, 4976640, 5160960, 5308416, 5529600, 5598720, 5806080, 5898240, 5971968, 6220800, 6291456, 6531840, 6635520, 6718464, 6912000, 7077888, 7257600, 7372800, 7464960, 7741440, 7864320, 7962624, 8294400, 8388608, 8709120, 8847360, 8957952, 9437184, 9676800, 9953280, 10077696, 10321920, 10368000, 10616832, 11059200, 11197440, 11612160, 11796480, 11943936, 12441600, 12582912, 13063680, 13271040, 13436928, 13824000, 14155776, 14515200, 14745600, 14929920, 15482880, 15728640, 15925248, 16588800, 16777216, 17418240, 17694720, 17915904, 18662400, 18874368, 19353600, 19906560, 20155392, 20643840.

Some larger examples :