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%I #5 Sep 19 2018 09:16:48
%S 1,1,1,1,2,1,3,2,3,4,5,4,6,7,7,9,11,12,12,15,17,20,22,24,25,31,35,39,
%T 40,48,51,55,64,73,77,85,92,104,115,126,136,147,157,176,198,211,234,
%U 246,269,294,326,350,375,403,443,475,526,560,600,650
%N Number of integer partitions of n such that every distinct submultiset has a different LCM.
%C Note that such partitions are necessarily strict.
%e The a(19) = 12 partitions:
%e (19),
%e (10,9), (11,8), (12,7), (13,6), (14,5), (15,4), (16,3), (17,2),
%e (8,6,5), (11,5,3),
%e (7,5,4,3).
%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&UnsameQ@@LCM@@@Union[Rest[Subsets[#]]]&]],{n,30}]
%Y Cf. A074761, A108917, A275972, A290103, A316313, A316429, A316431, A319315, A319318, A319327.
%K nonn
%O 1,5
%A _Gus Wiseman_, Sep 17 2018
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