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 A293627 #19 Oct 29 2017 21:30:13
%S A293627 1,1,1,2,2,4,4,6,8,11,12,19,21,27,34,45,51,69,77,100,117,146
%N A293627 Number of knapsack factorizations whose factors sum to n.
%C A293627 A knapsack factorization is a finite multiset of positive integers greater than one such that every distinct submultiset has a different product.
%e A293627 The a(12) = 19 partitions are:
%e A293627 (12),
%e A293627 (10 2), (9 3), (8 4), (7 5), (6 6),
%e A293627 (8 2 2), (7 3 2), (6 4 2), (6 3 3), (5 5 2), (5 4 3), (4 4 4),
%e A293627 (6 2 2 2), (5 3 2 2), (4 3 3 2), (3 3 3 3),
%e A293627 (3 3 2 2 2),
%e A293627 (2 2 2 2 2 2).
%t A293627 nn=22;
%t A293627 apsQ[y_]:=UnsameQ@@Times@@@Union[Rest@Subsets[y]];
%t A293627 Table[Length@Select[IntegerPartitions[n],apsQ],{n,nn}]
%Y A293627 Cf. A000041, A001055, A002033, A002865, A108917, A126796, A275972, A281116, A292886, A294150.
%K A293627 nonn,more
%O A293627 1,4
%A A293627 _Gus Wiseman_, Oct 23 2017