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%I #8 Sep 15 2018 15:47:21
%S 1,2,3,4,5,7,8,9,11,12,13,16,17,18,19,20,23,24,25,27,28,29,31,32,37,
%T 40,41,43,44,45,47,48,49,50,52,53,54,56,59,60,61,63,64,67,68,71,72,73,
%U 75,76,79,80,81,83,84,88,89,90,92,96,97,98,99,101,103,104
%N Numbers whose prime multiplicities appear with relatively prime multiplicities.
%C Numbers 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: (), (1), (2), (11), (3), (4), (111), (22), (5), (211), (6), (1111), (7), (221), (8), (311), (9), (2111), (33), (222), (411).
%t Select[Range[100],GCD@@Length/@Split[Sort[FactorInteger[#][[All,2]]]]==1&]
%Y Cf. A001597, A007916, A056239, A072774, A181819, A182850, A289509, A296150, A298748, A305732, A319151, A319160, A319163, A319165.
%K nonn
%O 1,2
%A _Gus Wiseman_, Sep 12 2018
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