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

1,1

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