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%I #7 Sep 15 2018 15:47:38
%S 4,8,9,16,25,27,32,49,64,81,121,125,128,144,169,243,256,289,324,343,
%T 361,400,512,529,576,625,729,784,841,961,1024,1331,1369,1600,1681,
%U 1728,1849,1936,2025,2048,2187,2197,2209,2304,2401,2500,2704,2809,2916,3125
%N Perfect powers whose prime multiplicities appear with relatively prime multiplicities.
%C Perfect powers n such that A181819(n) is not a perfect power (i.e. belongs to A007916).
%e The sequence of integer partitions whose Heinz numbers are in the sequence begins: (11), (111), (22), (1111), (33), (222), (11111), (44), (111111), (2222), (55), (333), (1111111), (221111), (66), (22222), (11111111), (77), (222211), (444), (88), (331111), (111111111), (99), (22111111), (3333), (222222), (441111).
%t Select[Range[1000],And[GCD@@FactorInteger[#][[All,2]]>1,GCD@@Length/@Split[Sort[FactorInteger[#][[All,2]]]]==1]&]
%Y Cf. A001597, A007916, A056239, A072774, A181819, A289509, A296150, A298748, A319151, A319161, A319162, A319165.
%K nonn
%O 1,1
%A _Gus Wiseman_, Sep 12 2018