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 A292886 #15 Oct 29 2017 02:35:50
%S A292886 1,1,1,2,1,2,1,3,2,2,1,4,1,2,2,4,1,4,1,4,2,2,1,7,2,2,3,4,1,5,1,6,2,2,
%T A292886 2,8,1,2,2,7,1,5,1,4,4,2,1,11,2,4,2,4,1,7,2,7,2,2,1,11,1,2,4,7,2,5,1,
%U A292886 4,2,5,1,15,1,2,4,4,2,5,1,11,4,2,1,11,2
%N A292886 Number of knapsack factorizations of n.
%C A292886 A knapsack factorization is a finite multiset of positive integers greater than one such that every distinct submultiset has a different product.
%C A292886 The sequence giving the number of factorizations of n is described as "the multiplicative partition function" (see A001055), so knapsack factorizations are a multiplicative generalization of knapsack partitions. - _Gus Wiseman_, Oct 24 2017
%H A292886 Vincenzo Librandi, <a href="/A292886/b292886.txt">Table of n, a(n) for n = 1..2000</a>
%e A292886 The a(36) = 8 factorizations are 2*2*3*3, 2*2*9, 2*18, 3*3*4, 3*12, 4*9, 6*6, 36. The factorization 2*3*6 is not knapsack.
%t A292886 postfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[postfacs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A292886 Table[Length[Select[postfacs[n],UnsameQ@@Times@@@Union[Subsets[#]]&]],{n,100}]
%Y A292886 Cf. A001055, A045778, a(p^n) = A108917(n), A162247, A259936, A275972, A281116.
%K A292886 nonn
%O A292886 1,4
%A A292886 _Gus Wiseman_, Sep 26 2017