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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

EXAMPLE

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.

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]

CROSSREFS

Subsequence of A083207.

Sequence in context: A044628 A181190 A246474 * A336628 A336443 A252954

Adjacent sequences:  A334404 A334405 A334406 * A334408 A334409 A334410

KEYWORD

nonn

AUTHOR

Amiram Eldar, Apr 27 2020

STATUS

approved

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Last modified December 7 20:40 EST 2021. Contains 349589 sequences. (Running on oeis4.)