A364053 Zumkeller numbers whose divisors can be partitioned into two disjoint sets with equal products.

6, 24, 30, 40, 42, 54, 56, 60, 66, 70, 78, 84, 88, 90, 96, 102, 104, 108, 114, 120, 126, 132, 138, 140, 150, 156, 160, 168, 174, 186, 198, 204, 210, 216, 220, 222, 224, 228, 234, 240, 246, 258, 260, 264, 270, 276, 280, 282, 294, 306, 308, 312, 318, 330, 336, 340, 342, 348, 350, 352

Offset: 1

Author

Ivan N. Ianakiev, Jul 04 2023

Keywords

• nonn

Comments

Intersection of A083207 and A048943.

Examples

			The divisors of 24 are {1,2,3,4,6,8,12,24}. They can be partitioned into two disjoint sets with equal sums, namely {4,6,8,12} and {1,2,3,24}, and two disjoint sets with equal products, namely {1,2,12,24} and {3,4,6,8}. So, 24 is a term and also a term of A347063.
		

Crossrefs

Cf. A083207, A048943, A347063.

Programs

Mathematica

zQ[n_]:=Module[{d=Divisors[n],t,ds,x},ds=Plus@@d;If[Mod[ds,2]>0,False,t=CoefficientList[Product[1+x^i,{i,d}],x];t[[1+ds/2]]>0]]; fQ[n_]:=IntegerQ[Sqrt[Times@@Divisors[n]]];
Select[Range[1000],And[fQ[#],zQ[#]]&] (*zQ and fQ by T. D. Noe at A083207 and A048943*)