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Jordan-Polya n.  and  powerful n.

First numbers that belong to both sets:

1, 4, 8, 16, 32, 36, 64, 72, 128, 144, 216, 256, 288, 432, 512, 576, 864, 1024, 1152, 1296, 1728, 2048, 2304, 2592, 3456, 4096, 4608, 5184, 6912, 7776, 8192, 9216, 10368, 13824, 14400, 15552, 16384, 18432, 20736, 27648, 28800, 31104, 32768, 36864, 41472, 46656, 55296, 57600, 62208, 65536, 73728, 82944, 86400, 93312, 110592, 115200, 124416, 131072, 147456, 165888, 172800, 186624, 221184, 230400, 248832, 262144, 279936, 294912, 331776, 345600, 373248, 442368, 460800, 497664, 518400, 524288, 559872, 589824, 663552, 691200, 746496, 884736, 921600, 995328, 1036800, 1048576, 1119744, 1179648, 1327104, 1382400, 1492992, 1679616, 1728000, 1769472, 1843200, 1990656, 2073600, 2097152, 2239488, 2359296, 2654208, 2764800, 2985984, 3110400, 3359232, 3456000, 3538944, 3686400, 3981312, 4147200, 4194304, 4478976, 4718592, 5308416, 5529600, 5971968, 6220800, 6718464, 6912000, 7077888, 7372800, 7962624, 8294400, 8388608, 8957952, 9437184, 10077696, 10368000, 10616832, 11059200, 11943936, 12441600, 13436928, 13824000, 14155776, 14745600, 15925248, 16588800, 16777216, 17915904, 18662400, 18874368, 20155392, 20736000, 21233664, 22118400, 23887872, 24883200, 25401600, 26873856, 27648000, 28311552, 29491200, 31850496, 33177600, 33554432, 35831808, 37324800, 37748736, 40310784, 41472000, 42467328, 44236800, 47775744, 49766400, 50803200, 53747712, 55296000, 56623104, 58982400, 60466176, 62208000, 63700992, 66355200, 67108864, 71663616, 74649600, 75497472, 80621568, 82944000, 84934656, 88473600, 95551488, 99532800, 101606400, 107495424, 110592000, 111974400, 113246208, 117964800, 120932352, 124416000, 127401984, 132710400, 134217728, 143327232, 149299200, 150994944, 152409600, 161243136, 165888000, 169869312, 176947200, 191102976, 199065600, 203212800, 207360000, 214990848, 221184000, 223948800, 226492416, 235929600, 241864704, 248832000, 254803968, 265420800, 268435456, 286654464, 298598400, 301989888, 304819200, 322486272, 331776000, 339738624, 353894400, 362797056, 373248000, 382205952, 398131200, 406425600, 414720000, 429981696, 442368000, 447897600, 452984832, 471859200, 483729408, 497664000, 509607936, 530841600, 536870912, 573308928, 597196800, 603979776, 609638400, 644972544, 663552000, 671846400, 679477248, 707788800, 725594112, 746496000, 764411904, 796262400, 812851200, 829440000, 859963392, 884736000, 895795200, 905969664, 914457600, 943718400, 967458816, 995328000, 1019215872, 1061683200, 1073741824, 1146617856, 1194393600, 1207959552, 1219276800, 1244160000, 1289945088, 1327104000, 1343692800, 1358954496, 1415577600, 1451188224, 1492992000, 1528823808.

Some larger examples :