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 A317656 #6 Aug 03 2018 08:17:12
%S A317656 0,1,1,1,1,2,1,3,1,2,1,8,1,2,2,10,1,8,1,8,2,2,1,35,1,2,3,8,1,15,1,37,
%T A317656 2,2,2,50,1,2,2,35,1,15,1,8,8,2,1,160,1,8,2,8,1,35,2,35,2,2,1,96,1,2,
%U A317656 8,144,2,15,1,8,2,15,1,299,1,2,8,8,2,15,1,160
%N A317656 Number of free pure symmetric multifunctions whose leaves are the integer partition with Heinz number n.
%C A317656 A free pure symmetric multifunction f in EPSM is either (case 1) a positive integer, or (case 2) an expression of the form h[g_1, ..., g_k] where k > 0, h is in EPSM, each of the g_i for i = 1, ..., k is in EPSM, and for i < j we have g_i <= g_j under a canonical total ordering of EPSM, such as the Mathematica ordering of expressions.
%e A317656 The a(12) = 8 free pure symmetric multifunctions are 1[1[2]], 1[2[1]], 1[1,2], 2[1[1]], 2[1,1], 1[1][2], 1[2][1], 2[1][1].
%t A317656 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A317656 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A317656 exprUsing[m_]:=exprUsing[m]=If[Length[m]==0,{},If[Length[m]==1,{First[m]},Join@@Cases[Union[Table[PR[m[[s]],m[[Complement[Range[Length[m]],s]]]],{s,Take[Subsets[Range[Length[m]]],{2,-2}]}]],PR[h_,g_]:>Join@@Table[Apply@@@Tuples[{exprUsing[h],Union[Sort/@Tuples[exprUsing/@p]]}],{p,mps[g]}]]]];
%t A317656 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A317656 Table[Length[exprUsing[primeMS[n]]],{n,100}]
%Y A317656 Cf. A001003, A052893, A053492, A255906, A277996, A279944, A280000.
%Y A317656 Cf. A317652, A317653, A317654, A317655, A317658.
%K A317656 nonn
%O A317656 1,6
%A A317656 _Gus Wiseman_, Aug 03 2018