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 A321177 #5 Dec 08 2018 21:04:55
%S A321177 1,4,8,12,16,18,24,27,32,36,40
%N A321177 Heinz numbers of integer partitions that are the vertex-degrees of some set system with no singletons.
%C A321177 A set system is a finite set of finite nonempty sets.
%C A321177 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%e A321177 Each term paired with its Heinz partition and a realizing set system:
%e A321177 1: (): {}
%e A321177 4: (11): {{1,2}}
%e A321177 8: (111): {{1,2,3}}
%e A321177 12: (211): {{1,2},{1,3}}
%e A321177 16: (1111): {{1,2,3,4}}
%e A321177 18: (221): {{1,2},{1,2,3}}
%e A321177 24: (2111): {{1,2},{1,3,4}}
%e A321177 27: (222): {{1,2},{1,3},{2,3}}
%e A321177 32: (11111): {{1,2,3,4,5}}
%e A321177 36: (2211): {{1,2},{1,2,3,4}}
%e A321177 40: (3111): {{1,2},{1,3},{1,4}}
%t A321177 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A321177 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A321177 hyp[m_]:=Select[mps[m],And[And@@UnsameQ@@@#,UnsameQ@@#,Min@@Length/@#>1]&];
%t A321177 nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]],{#1}]&,If[n==1,{},Flatten[Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t A321177 Select[Range[20],!hyp[nrmptn[#]]=={}&]
%Y A321177 Cf. A000070, A000569, A056239, A112798, A283877, A306005, A318361, A320922, A320923, A320924, A320925, A321176.
%K A321177 nonn,more
%O A321177 1,2
%A A321177 _Gus Wiseman_, Oct 29 2018