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%I #8 Jul 15 2018 13:25:09
%S 1,2,3,5,7,11,12,13,17,18,19,20,23,24,28,29,31,37,40,41,43,44,45,47,
%T 48,50,52,53,54,56,59,61,63,67,68,71,72,73,75,76,79,80,83,88,89,92,96,
%U 97,98,99,101,103,104,107,108,109,112,113,116,117,124,127,131
%N Numbers whose prime multiplicities are distinct and relatively prime.
%C A subsequence of A007916.
%e 60 = 2^2 * 3^1 * 5^1 has prime multiplicities (2,1,1), which are relatively prime but not distinct, so 60 does not belong to the sequence.
%e 72 = 2^3 * 3^2 has prime multiplicities (3,2), which are distinct and relatively prime, so 72 belongs to the sequence.
%e 144 = 2^4 * 3^2 has prime multiplicities (4,2), which are distinct but not relatively prime, so 144 does not belong to the sequence.
%t Select[Range[100],And[UnsameQ@@Last/@FactorInteger[#],GCD@@Last/@FactorInteger[#]==1]&]
%Y Cf. A000837, A005117, A007916, A130091, A301700, A303431, A316794, A316795, A316796.
%K nonn
%O 1,2
%A _Gus Wiseman_, Jul 14 2018
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