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 A316401 #4 Jul 01 2018 21:18:25
%S A316401 0,0,0,0,0,0,0,1,0,2,0,1,0,3,1,3,2,4,2,6,6,11,9,9,10,20,16,18,17,27,
%T A316401 24,31,29,43,31,43,40,59,52,58,61,83,68,93,80,124,99,120,109,145,151,
%U A316401 185,160,232,163,257,229,314,280,286,310,427,385,513,333,596
%N A316401 Number of strict integer partitions of n that are not knapsack (not every subset has a different sum) but every subset has a different average.
%e A316401 The a(22) = 11 partitions:
%e A316401 (11,6,5), (11,7,4), (11,8,3), (11,9,2), (11,10,1),
%e A316401 (11,5,4,2), (11,6,3,2), (11,8,2,1), (12,5,3,2), (12,5,4,1), (14,4,3,1).
%t A316401 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&!UnsameQ@@Total/@Union[Subsets[#]]&&UnsameQ@@Mean/@Union[Subsets[#]]&]],{n,20}]
%Y A316401 Cf. A000009, A108917, A275972, A299702, A301899, A301900, A316271, A316313, A316314, A316399, A316400.
%K A316401 nonn
%O A316401 1,10
%A A316401 _Gus Wiseman_, Jul 01 2018