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%I #6 Oct 11 2018 10:10:03
%S 7,9,14,18,19,21,23,25,27,28,36,38,42,46,49,50,53,54,56,57,63,72,76,
%T 81,84,92,97,98,100,103,106,108,112,114,115,121,125,126,131,133,144,
%U 147,151,152,159,161,162,168,169,171,175,183,184,185,189,194,195,196
%N Numbers whose product of prime indices is a perfect power.
%C A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%e The terms together with their corresponding multiset multisystems (A302242):
%e 7: {{1,1}}
%e 9: {{1},{1}}
%e 14: {{},{1,1}}
%e 18: {{},{1},{1}}
%e 19: {{1,1,1}}
%e 21: {{1},{1,1}}
%e 23: {{2,2}}
%e 25: {{2},{2}}
%e 27: {{1},{1},{1}}
%e 28: {{},{},{1,1}}
%e 36: {{},{},{1},{1}}
%e 38: {{},{1,1,1}}
%e 42: {{},{1},{1,1}}
%e 46: {{},{2,2}}
%e 49: {{1,1},{1,1}}
%e 50: {{},{2},{2}}
%e 53: {{1,1,1,1}}
%e 54: {{},{1},{1},{1}}
%e 56: {{},{},{},{1,1}}
%e 57: {{1},{1,1,1}}
%e 63: {{1},{1},{1,1}}
%e 72: {{},{},{},{1},{1}}
%e 76: {{},{},{1,1,1}}
%e 81: {{1},{1},{1},{1}}
%t Select[Range[100],GCD@@FactorInteger[Times@@Cases[FactorInteger[#],{p_,k_}:>PrimePi[p]^k]][[All,2]]>1&]
%Y Cf. A000720, A001222, A001597, A003963, A056239, A064573, A112798, A302242, A305551, A306017, A319056, A319066, A320322, A320323, A320324.
%K nonn
%O 1,1
%A _Gus Wiseman_, Oct 10 2018
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