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 A323091 #6 Jan 04 2019 17:33:08
%S A323091 1,1,1,1,1,2,1,2,1,2,1,3,1,2,2,2,1,3,1,3,2,2,1,5,1,2,2,3,1,5,1,3,2,2,
%T A323091 2,4,1,2,2,5,1,5,1,3,3,2,1,7,1,3,2,3,1,5,2,5,2,2,1,9,1,2,3,3,2,5,1,3,
%U A323091 2,5,1,9,1,2,3,3,2,5,1,7,2,2,1,9,2,2,2
%N A323091 Number of strict knapsack factorizations of n.
%C A323091 A strict knapsack factorization is a finite set of positive integers > 1 such that every subset has a different product.
%F A323091 a(prime^n) = A275972(n).
%e A323091 The a(144) = 11 factorizations:
%e A323091 (144),
%e A323091 (2*72), (3*48), (4*36),(6*24), (8*18), (9*16),
%e A323091 (2*3*24), (2*4*18), (2*8*9), (3*6*8).
%e A323091 Missing from this list are (2*6*12), (3*4*12), (2*3*4*6), which are not knapsack.
%t A323091 strfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[strfacs[n/d],Min@@#>d&]],{d,Rest[Divisors[n]]}]];
%t A323091 Table[Length[Select[strfacs[n],UnsameQ@@Times@@@Subsets[#]&]],{n,100}]
%Y A323091 Cf. A001055, A045778, A108917, A120641, A275972, A292886, A305150, A323087.
%K A323091 nonn
%O A323091 1,6
%A A323091 _Gus Wiseman_, Jan 04 2019