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 A322369 #4 Dec 05 2018 07:58:48
%S A322369 1,0,0,1,1,2,2,4,4,6,7,10,10,16,17,22,26,33,36,48,52,64,76,90,101,125,
%T A322369 142,166,192,225,250,302,339,393,451,515,581,675,762,866,985,1122,
%U A322369 1255,1441,1612,1823,2059,2318,2591,2930,3275,3668,4118,4605,5125,5749
%N A322369 Number of strict disconnected or empty integer partitions of n.
%C A322369 An integer partition is connected if the prime factorizations of its parts form a connected hypergraph. It is disconnected if it can be separated into two or more integer partitions with relatively prime products. For example, the integer partition (654321) has three connected components: (6432)(5)(1).
%e A322369 The a(3) = 1 through a(11) = 10 strict disconnected integer partitions:
%e A322369 (2,1) (3,1) (3,2) (5,1) (4,3) (5,3) (5,4) (7,3) (6,5)
%e A322369 (4,1) (3,2,1) (5,2) (7,1) (7,2) (9,1) (7,4)
%e A322369 (6,1) (4,3,1) (8,1) (5,3,2) (8,3)
%e A322369 (4,2,1) (5,2,1) (4,3,2) (5,4,1) (9,2)
%e A322369 (5,3,1) (6,3,1) (10,1)
%e A322369 (6,2,1) (7,2,1) (5,4,2)
%e A322369 (4,3,2,1) (6,4,1)
%e A322369 (7,3,1)
%e A322369 (8,2,1)
%e A322369 (5,3,2,1)
%t A322369 zsm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[Less@@#,GCD@@s[[#]]]>1&]},If[c=={},s,zsm[Sort[Append[Delete[s,List/@c[[1]]],LCM@@s[[c[[1]]]]]]]]];
%t A322369 Table[Length[Select[IntegerPartitions[n],And[UnsameQ@@#,Length[zsm[#]]!=1]&]],{n,30}]
%Y A322369 Cf. A054921, A218970, A286518, A304714, A304716, A305078, A305079, A322306, A322307, A322335, A322337, A322338, A322367, A322368.
%K A322369 nonn
%O A322369 0,6
%A A322369 _Gus Wiseman_, Dec 04 2018