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 A303674 #52 Sep 16 2018 04:42:36
%S A303674 1,1,1,2,1,3,1,3,2,4,1,4,1,6,4,5,1,8,2,7,5,11,3,11,5,13,6,14,7,19,6,
%T A303674 19,15,24,13,28,15,33,20,34,22,46,30,48,32,57,39,67,48,76,63,88,62,
%U A303674 104,88,110,94,130,115,164,121,172,152,198,176,229,203,270,235,293,272,341,311,375,349,453,420,506,452,570,547
%N A303674 Number of connected integer partitions of n > 1 whose distinct parts are pairwise indivisible and whose z-density is -1.
%C A303674 The z-density of a multiset S is defined to be Sum_{s in S} (omega(s) - 1) - omega(lcm(S)), where omega = A001221 and lcm is least common multiple.
%C A303674 Given a finite multiset S of positive integers greater than 1, let G(S) be the simple labeled graph with vertex set S and edges between any two vertices that have a common divisor greater than 1. 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 A303674 The a(18) = 8 integer partitions are (18), (14,4), (10,8), (9,9), (10,4,4), (6,4,4,4), (3,3,3,3,3,3), (2,2,2,2,2,2,2,2,2).
%e A303674 The a(20) = 7 integer partitions are (20), (14,6), (12,8), (10,6,4), (5,5,5,5), (4,4,4,4,4), (2,2,2,2,2,2,2,2,2,2).
%t A303674 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 A303674 zensity[s_]:=Total[(PrimeNu[#]-1&)/@s]-PrimeNu[LCM@@s];
%t A303674 Table[Length[Select[IntegerPartitions[n],And[zensity[#]==-1,Length[zsm[#]]==1,Select[Tuples[#,2],UnsameQ@@#&&Divisible@@#&]=={}]&]],{n,30}]
%Y A303674 Cf. A030019, A035053, A048143, A134954, A286520, A293510, A293994, A303837, A303838, A304382.
%K A303674 nonn
%O A303674 1,4
%A A303674 _Gus Wiseman_, Jun 04 2018
%E A303674 a(51)-a(81) from _Robert Price_, Sep 15 2018