The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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