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 A319318 #6 Sep 19 2018 09:15:49
%S A319318 1,1,1,1,2,1,3,2,3,3,5,2,6,5,5,5,8,5,9,6,8,9,11,6,11,11,11,10,14,9,16,
%T A319318 12,14,15,15,11,19,17,17,14,22,15,22,18,18,21,25,16,24,21,23,22,28,21,
%U A319318 26,22,26,27,32,20,35,30,27,27,31,27,38,30,33,29
%N A319318 Number of integer partitions of n such that every distinct submultiset has a different GCD.
%C A319318 Note that such partitions are necessarily strict.
%e A319318 The a(31) = 16 partitions are (31), (16,15), (17,14), (18,13), (19,12), (20,11), (21,10), (22,9), (23,8), (24,7), (25,6), (26,5), (27,4), (28,3), (29,2), (15,10,6).
%t A319318 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&UnsameQ@@GCD@@@Union[Rest[Subsets[#]]]&]],{n,30}]
%Y A319318 Cf. A108917, A275972, A289508, A289509, A316313, A319315, A319319, A319320.
%K A319318 nonn
%O A319318 1,5
%A A319318 _Gus Wiseman_, Sep 17 2018