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 A381874 #4 Mar 12 2025 08:40:15
%S A381874 24,30,42,54,60,66,78,84,90,96,102,108,114,120,126,132,138,140,150,
%T A381874 156,160,168,174,186,198,204,210,216,220,222,224,228,240,246,258,260,
%U A381874 264,270,276,280,282,306,308,312,318,330,336,340,342,348,352,354,360,364,366,372,378,380,384,390,402
%N A381874 Numbers whose set of divisors can be partitioned: a) into two disjoint subsets with equal sums and cardinalities, and b) into two disjoint subsets with equal products and cardinalities.
%C A381874 If y is a term of this sequence, then so is p*y, where p is a prime that is coprime to y.
%C A381874 It seems that the maximum first difference is 24.
%e A381874 Let D be the set of the divisors of 24, i.e. {1,2,3,4,6,8,12,24}. On the one hand (sums) D = {1,2,3,24} union {4,6,8,12}. On the other hand (products) D = {1,2,12,24} union {3,4,6,8}. So, 24 is a term.
%t A381874 sumQ[set_]:=AnyTrue[Subsets[set,{Length[set]/2}],(Plus@@#==Total[Complement[set,#]]&)];
%t A381874 prodQ[set_]:=AnyTrue[Subsets[set,{Length[set]/2}],(Times@@#==Times@@Complement[set,#]&)];
%t A381874 Select[Range[500],sumQ[Divisors[#]]&&prodQ[Divisors[#]]&]//Quiet
%Y A381874 Cf. A083207 (supersequence), A347063 (supersequence).
%K A381874 nonn
%O A381874 1,1
%A A381874 _Ivan N. Ianakiev_, Mar 09 2025