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 A304714 #8 Nov 30 2019 16:59:10
%S A304714 1,1,1,1,1,2,1,2,2,3,2,5,2,5,5,6,5,10,6,12,12,13,14,21,17,23,26,30,31,
%T A304714 46,38,51,55,61,70,87,85,102,116,128,138,171,169,204,225,245,272,319,
%U A304714 334,383,429,464,515,593,629,715,790,861,950,1082
%N A304714 Number of connected strict integer partitions of n.
%C A304714 Given a finite set S of positive integers greater than one, let G(S) be the simple labeled graph with vertex set S and edges between any two vertices with a common divisor. For example, G({6,14,15,35}) is a 4-cycle. A multiset S is said to be connected if G(S) is a connected graph.
%e A304714 The a(19) = 6 strict integer partitions are (19), (9,6,4), (10,5,4), (10,6,3), (12,4,3), (8,6,3,2). Taking the normalized prime factors of each part (see A112798, A302242), we have the following connected multiset multisystems.
%e A304714 (19): {{8}}
%e A304714 (9,6,4): {{2,2},{1,2},{1,1}}
%e A304714 (10,5,4): {{1,3},{3},{1,1}}
%e A304714 (10,6,3): {{1,3},{1,2},{2}}
%e A304714 (12,4,3): {{1,1,2},{1,1},{2}}
%e A304714 (8,6,3,2): {{1,1,1},{1,2},{2},{1}}
%t A304714 zsm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[Less@@#,GCD@@s[[#]]]>1&]},If[c==={},s,zsm[Union[Append[Delete[s,List/@c[[1]]],LCM@@s[[c[[1]]]]]]]]];
%t A304714 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Length[zsm[#]]===1&]],{n,60}]
%Y A304714 The Heinz numbers of these partitions are given by A328513.
%Y A304714 Cf. A000009, A003963, A048143, A054921, A076078, A259936, A281116, A285572, A285573, A286518, A286520, A302242.
%K A304714 nonn
%O A304714 1,6
%A A304714 _Gus Wiseman_, May 17 2018