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%I #23 May 13 2018 08:25:52
%S 4,8,16,32,36,64,128,144,216,256,324,512,576,900,1024,1296,1728,2048,
%T 2304,2916,3600,4096,5184,5832,7776,8100,8192,9216,11664,13824,14400,
%U 16384,20736,22500,26244,27000,32400,32768,36864,44100,46656,57600,65536,72900
%N Perfect powers whose prime factors span an initial interval of prime numbers.
%C The multiset of prime indices of a(n) is the a(n)-th row of A112798. This multiset is normal, meaning it spans an initial interval of positive integers, and periodic, meaning its multiplicities have a common divisor greater than 1.
%F Intersection of A001597 and A055932.
%e Sequence of all normal periodic multisets begins
%e 4: {1,1}
%e 8: {1,1,1}
%e 16: {1,1,1,1}
%e 32: {1,1,1,1,1}
%e 36: {1,1,2,2}
%e 64: {1,1,1,1,1,1}
%e 128: {1,1,1,1,1,1,1}
%e 144: {1,1,1,1,2,2}
%e 216: {1,1,1,2,2,2}
%e 256: {1,1,1,1,1,1,1,1}
%e 324: {1,1,2,2,2,2}
%e 512: {1,1,1,1,1,1,1,1,1}
%e 576: {1,1,1,1,1,1,2,2}
%e 900: {1,1,2,2,3,3}
%e 1024: {1,1,1,1,1,1,1,1,1,1}
%t Select[Range[1000],FactorInteger[#][[-1,1]]==Prime[Length[FactorInteger[#]]]&&GCD@@FactorInteger[#][[All,2]]>1&]
%Y Cf. A000837, A000961 A001597, A007916, A018783, A052409, A052410, A055932, A056239, A112798, A178472, A303431, A303709, A304450.
%K nonn
%O 1,1
%A _Gus Wiseman_, May 13 2018
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