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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. 2

%I

%S 60,140,160,168,180,216,220,252,260,300,312,340,360,380,396,420,432,

%T 460,462,480,500,504,520,540,580,600,616,620,624,630,660,672,684,720,

%U 728,740,756,780,792,810,820,840,858,860,864,870,924,936,940,960,990,1008,1020

%N 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.

%H Amiram Eldar, <a href="/A334407/b334407.txt">Table of n, a(n) for n = 1..1000</a>

%e 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.

%t 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]

%Y Subsequence of A083207.

%K nonn

%O 1,1

%A _Amiram Eldar_, Apr 27 2020

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Last modified January 25 03:44 EST 2022. Contains 350565 sequences. (Running on oeis4.)