%I #5 Sep 15 2018 15:48:15
%S 4,8,16,32,36,64,100,128,144,196,216,225,256,324,400,484,512,576,676,
%T 784,900,1000,1024,1089,1156,1225,1296,1444,1600,1728,1764,1936,2025,
%U 2048,2116,2304,2500,2601,2704,2744,2916,3025,3136,3364,3375,3600,3844,4096
%N Perfect powers whose prime indices are relatively prime.
%C A prime index of n is a number m such that prime(m) divides n.
%e The sequence of integer partitions whose Heinz numbers are in the sequence begins: (11), (111), (1111), (11111), (2211), (111111), (3311), (1111111), (221111), (4411), (222111), (3322), (11111111), (222211), (331111), (5511), (111111111), (22111111), (6611), (441111), (332211), (333111).
%t Select[Range[1000],And[GCD@@PrimePi/@FactorInteger[#][[All,1]]==1,GCD@@FactorInteger[#][[All,2]]>1]&]
%Y Cf. A001597, A056239, A072774, A289509, A298748, A319161, A319163, A319165, A319179, A319181.
%K nonn
%O 1,1
%A _Gus Wiseman_, Sep 12 2018