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%I A294150 #8 Oct 29 2017 21:30:37
%S A294150 1,1,1,2,2,4,4,6,8,10,12,13,20,20,29,30,41,41,56,53,81,75
%N A294150 Number of knapsack partitions of n that are also knapsack factorizations.
%C A294150 a(n) is the number of finite multisets of positive integers summing to n such that every distinct submultiset has a different sum, and also every distinct submultiset has a different product.
%H A294150 R. Ehrenborg and M. Readdy, <a href="http://dx.doi.org/10.1016/j.aam.2006.08.006">The Mobius function of partitions with restricted block sizes</a>, Advances in Applied Mathematics, Volume 39, Issue 3, September 2007, Pages 283-292.
%e A294150 The a(12) = 13 partitions are:
%e A294150 (12),
%e A294150 (10 2), (9 3), (8 4), (7 5), (6 6),
%e A294150 (8 2 2), (7 3 2), (5 5 2), (5 4 3), (4 4 4),
%e A294150 (3 3 3 3),
%e A294150 (2 2 2 2 2 2).
%t A294150 nn=22;
%t A294150 dubQ[y_]:=And[UnsameQ@@Times@@@Union[Rest@Subsets[y]],UnsameQ@@Plus@@@Union[Rest@Subsets[y]]];
%t A294150 Table[Length@Select[IntegerPartitions[n],dubQ],{n,nn}]
%Y A294150 Cf. A000041, A001055, A108917, A275972, A292886, A293627.
%K A294150 nonn,more
%O A294150 1,4
%A A294150 _Gus Wiseman_, Oct 23 2017

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