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%I #4 Sep 15 2018 15:47:57
%S 9,25,27,49,81,121,125,169,243,289,343,361,441,529,625,729,841,961,
%T 1331,1369,1521,1681,1849,2187,2197,2209,2401,2809,3125,3249,3481,
%U 3721,3969,4225,4489,4913,5041,5329,6241,6561,6859,6889,7569,7921,8281,9261,9409
%N Perfect powers whose prime indices are not 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: (22), (33), (222), (44), (2222), (55), (333), (66), (22222), (77), (444), (88), (4422), (99), (3333), (222222).
%t Select[Range[10000],With[{t=Transpose[FactorInteger[#]]},And[GCD@@PrimePi/@t[[1]]>1,GCD@@t[[2]]>1]]&]
%Y Cf. A001597, A056239, A072774, A181819, A289509, A296150, A298748, A319151, A319161, A319163, A319164.
%K nonn
%O 1,1
%A _Gus Wiseman_, Sep 12 2018
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