A334407 Numbers k whose divisors can be partitioned into two disjoint sets with equal sum, such that if d is in one set, then k/d is in the other set.

60, 140, 160, 168, 180, 216, 220, 252, 260, 300, 312, 340, 360, 380, 396, 420, 432, 460, 462, 480, 500, 504, 520, 540, 580, 600, 616, 620, 624, 630, 660, 672, 684, 720, 728, 740, 756, 780, 792, 810, 820, 840, 858, 860, 864, 870, 924, 936, 940, 960, 990, 1008, 1020

Offset: 1

Author

Amiram Eldar, Apr 27 2020

Keywords

• nonn

Examples

			60 is a term since its set of divisors can be partitioned into two disjoint subsets: {1, 6, 12, 15, 20, 30} and {60, 10, 5, 4, 3, 2} = {60/1, 60/6, 60/12, 60/15, 60/20, 60/30} with the equal sum of 84, and with no pair of complementary divisors (d, 60/d) in the same subset.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Subsequence of A083207.

Programs

Mathematica

seqQ[n_] := Module[{d = Divisors[n]}, nd = Length[d]; If[OddQ[nd], False, divpairs = d[[-1 ;; nd/2 + 1 ;; -1]] - d[[1 ;; nd/2]]; sd = Plus @@ divpairs; If[OddQ[sd], False, SeriesCoefficient[Series[Product[1 + x^divpairs[[i]], {i, Length[divpairs]}], {x, 0, sd/2}], sd/2] > 0]]]; Select[Range[1000], seqQ]