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 A319728 #6 Sep 26 2018 16:26:50
%S A319728 1,1,1,2,2,3,3,4,6,8,9,10,14,16,19,25,31,34,41,49,59,72,81,94,113,133,
%T A319728 152,179,209,239,273,315,366,422,478,548,627,711,812,926,1051,1185,
%U A319728 1340,1514,1718,1945,2179,2444,2757,3095,3465,3892,4362,4865,5427,6068
%N A319728 Number of strict T_0 integer partitions of n.
%C A319728 The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}. For an integer partition the T_0 condition means the dual of the multiset partition obtained by factoring each part into prime numbers is strict (no repeated blocks).
%e A319728 The a(11) = 10 integer partitions are (11), (7,4), (8,3), (9,2), (5,4,2), (6,3,2), (6,4,1), (7,3,1), (8,2,1), (5,3,2,1). Missing from this list are (6,5) and (10,1).
%t A319728 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]
%t A319728 dual[eds_]:=Table[First/@Position[eds,x],{x,Union@@eds}]
%t A319728 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&UnsameQ@@dual[primeMS/@#]&]],{n,60}]
%Y A319728 Cf. A000009, A000041, A001970, A007716, A059201, A305148, A316983, A319558, A319564, A319616.
%K A319728 nonn
%O A319728 0,4
%A A319728 _Gus Wiseman_, Sep 26 2018