This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A319320 #5 Sep 19 2018 09:16:48
%S A319320 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 A319320 40,48,51,55,64,73,77,85,92,104,115,126,136,147,157,176,198,211,234,
%U A319320 246,269,294,326,350,375,403,443,475,526,560,600,650
%N A319320 Number of integer partitions of n such that every distinct submultiset has a different LCM.
%C A319320 Note that such partitions are necessarily strict.
%e A319320 The a(19) = 12 partitions:
%e A319320 (19),
%e A319320 (10,9), (11,8), (12,7), (13,6), (14,5), (15,4), (16,3), (17,2),
%e A319320 (8,6,5), (11,5,3),
%e A319320 (7,5,4,3).
%t A319320 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&UnsameQ@@LCM@@@Union[Rest[Subsets[#]]]&]],{n,30}]
%Y A319320 Cf. A074761, A108917, A275972, A290103, A316313, A316429, A316431, A319315, A319318, A319327.
%K A319320 nonn
%O A319320 1,5
%A A319320 _Gus Wiseman_, Sep 17 2018