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%I #5 Apr 07 2017 01:39:23
%S 1,1,4,4,7,13,17,23,34,49,62,87,112,149,199,249,318,408,512,635,820,
%T 991,1238,1515,1864,2248,2770,3326,4030,4818,5808,6882,8290,9756,
%U 11639,13719,16236,18999,22468,26144,30724,35761,41754,48357,56380,65018,75438
%N Number of positive subset sums of strict integer partitions of n.
%C For a strict integer partition p summing to n, a pair (t,p) is defined to be a positive subset sum if there exists a nonempty subset of p summing to t.
%e The a(6)=13 subset sums are:
%e (6,6),
%e (1,51), (5,51), (6,51),
%e (2,42), (4,42), (6,42),
%e (1,321), (2,321), (3,321), (4,321), (5,321), (6,321).
%t nn=25;Total/@Table[Function[ptn,Length[Union[Total/@Rest[Subsets[ptn]]]]]/@Select[IntegerPartitions[n],UnsameQ@@#&],{n,nn}]
%Y Cf. A122768, A275972, A276024.
%K nonn
%O 1,3
%A _Gus Wiseman_, Mar 31 2017
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