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 A320889 #5 Oct 23 2018 21:01:07 %S A320889 1,1,1,1,1,2,1,2,1,2,1,3,1,2,2,2,1,3,1,3,2,2,1,5,1,2,2,3,1,5,1,3,2,2, %T A320889 2,6,1,2,2,5,1,5,1,3,3,2,1,7,1,3,2,3,1,5,2,5,2,2,1,9,1,2,3,5,2,5,1,3, %U A320889 2,5,1,9,1,2,3,3,2,5,1,7,2,2,1,9,2,2,2 %N A320889 Number of set partitions of strict factorizations of n into factors > 1 such that all the blocks have the same product. %e A320889 The a(144) = 17 set partitions: %e A320889 (2*3*4*6) (2*8*9) (2*72) (144) %e A320889 (2*6)*(3*4) (3*6*8) (3*48) %e A320889 (2*3*24) (4*36) %e A320889 (2*4*18) (6*24) %e A320889 (2*6*12) (8*18) %e A320889 (3*4*12) (9*16) %e A320889 (2*6)*(12) %e A320889 (3*4)*(12) %t A320889 strfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[strfacs[n/d],Min@@#>d&]],{d,Rest[Divisors[n]]}]]; %t A320889 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}]; %t A320889 Table[Length[Join@@Table[Select[sps[fac],SameQ@@Times@@@#&],{fac,strfacs[n]}]],{n,100}] %Y A320889 Cf. A000110, A001055, A001970, A045778, A050336, A279375, A294786, A294787, A296132, A320886, A320887, A320888. %K A320889 nonn %O A320889 1,6 %A A320889 _Gus Wiseman_, Oct 23 2018