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.

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

Offset: 1

Author

Amiram Eldar, Apr 27 2020

Keywords

• nonn

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, ...

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..680

Crossrefs

Subsequence of A290466.

Cf. A077610, A334407.

Programs

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]