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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.

%I A334408 #12 Apr 28 2020 05:56:34
%S A334408 462,858,870,1482,2310,2730,3570,3990,4002,4290,4620,4830,5460,5610,
%T A334408 6006,6090,6270,6438,6510,6630,6930,7140,7410,7770,7854,7998,8190,
%U A334408 8580,8610,8778,8970,9240,9570,9660,9870,10010,10230,10374,10626,10920,11220,11310,11550
%N 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.
%C A334408 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, ...
%H A334408 Amiram Eldar, <a href="/A334408/b334408.txt">Table of n, a(n) for n = 1..680</a>
%e A334408 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.
%t A334408 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]
%Y A334408 Subsequence of A290466.
%Y A334408 Cf. A077610, A334407.
%K A334408 nonn
%O A334408 1,1
%A A334408 _Amiram Eldar_, Apr 27 2020