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A364053
Zumkeller numbers whose divisors can be partitioned into two disjoint sets with equal products.
0
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
1,1
COMMENTS
Intersection of A083207 and A048943.
EXAMPLE
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.
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*)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ivan N. Ianakiev, Jul 04 2023
STATUS
approved