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!)
 A334408 Numbers k whose unitary 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. 1
 462, 858, 870, 1482, 2310, 2730, 3570, 3990, 4002, 4290, 4620, 4830, 5460, 5610, 6006, 6090, 6270, 6438, 6510, 6630, 6930, 7140, 7410, 7770, 7854, 7998, 8190, 8580, 8610, 8778, 8970, 9240, 9570, 9660, 9870, 10010, 10230, 10374, 10626, 10920, 11220, 11310, 11550 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The squarefree terms of A334407 are also terms of this sequence. Terms that are not squarefree are 4620, 5460, 6930, 7140, 8190, 8580, 9240, 9660, ... LINKS Amiram Eldar, Table of n, a(n) for n = 1..680 EXAMPLE 462 is a term since its set of unitary divisors can be partitioned into two disjoint subsets: {1, 11, 14, 22, 66, 77, 154, 231} and {462, 42, 33, 21, 7, 6, 3, 2} = {462/1, 462/11, 462/14, 462/22, 462/66, 462/77, 462/154, 462/231} with the equal sum of 576, and with no pair of complementary unitary divisors (d, 462/d) in the same subset. MATHEMATICA seqQ[n_] := Module[{d = Select[Divisors[n], CoprimeQ[#, n/#] &]}, nd = Length[d]; 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[2, 10000], seqQ] CROSSREFS Subsequence of A290466. Cf. A077610, A334407. Sequence in context: A104397 A108749 A267740 * A254468 A242321 A222342 Adjacent sequences:  A334405 A334406 A334407 * A334409 A334410 A334411 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 6 13:45 EST 2021. Contains 349563 sequences. (Running on oeis4.)