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 A325862 #5 Jun 02 2019 00:50:04
%S A325862 1,1,2,3,5,7,10,14,19,26,34,46,58,77,93,122,146,188,217,282,327,410,
%T A325862 470,596,673,848,947,1178,1325,1629,1798,2213,2444,2962,3247,3935,
%U A325862 4292,5149,5579,6674,7247,8590,9221,10964,11804,13870,14843,17480,18675,21866
%N A325862 Number of integer partitions of n such that every set of distinct parts has a different sum.
%C A325862 A knapsack partition (A108917, A299702) is an integer partition such that every submultiset has a different sum. The one non-knapsack partition counted under a(4) is (2,1,1).
%e A325862 The a(1) = 1 through a(7) = 14 partitions:
%e A325862 (1) (2) (3) (4) (5) (6) (7)
%e A325862 (11) (21) (22) (32) (33) (43)
%e A325862 (111) (31) (41) (42) (52)
%e A325862 (211) (221) (51) (61)
%e A325862 (1111) (311) (222) (322)
%e A325862 (2111) (411) (331)
%e A325862 (11111) (2211) (421)
%e A325862 (3111) (511)
%e A325862 (21111) (2221)
%e A325862 (111111) (4111)
%e A325862 (22111)
%e A325862 (31111)
%e A325862 (211111)
%e A325862 (1111111)
%e A325862 The three non-knapsack partitions counted under a(6) are:
%e A325862 (2,2,1,1)
%e A325862 (3,1,1,1)
%e A325862 (2,1,1,1,1)
%t A325862 Table[Length[Select[IntegerPartitions[n],UnsameQ@@Plus@@@Subsets[Union[#]]&]],{n,0,20}]
%Y A325862 Dominates A108917.
%Y A325862 Cf. A002033, A034444, A196723, A275972, A276024, A299702, A325592, A325856, A325863, A325864, A325865, A325877.
%K A325862 nonn
%O A325862 0,3
%A A325862 _Gus Wiseman_, May 31 2019