A348715 Numbers whose divisors can be partitioned into two disjoint sets without singletons whose harmonic means are both integers.

12, 18, 24, 30, 40, 42, 45, 48, 54, 56, 60, 66, 78, 84, 90, 96, 102, 114, 120, 126, 132, 135, 138, 140, 168, 174, 180, 186, 196, 198, 200, 204, 210, 222, 224, 234, 240, 246, 252, 258, 264, 270, 280, 282, 308, 318, 330, 336, 354, 360, 364, 366, 390, 396, 402, 420

Offset: 1

Author

Amiram Eldar, Oct 31 2021

Keywords

• nonn

Examples

			12 is a term since its set of divisors, {1, 2, 3, 4, 6, 12}, can be partitioned into the two disjoint sets, {1, 2, 3, 6} and {4, 12}, whose harmonic means, 2 and 6 respectively, are both integers.
		

Crossrefs

Cf. A001599, A027750, A083207.

Programs

Mathematica

hQ[d_] := IntegerQ @ HarmonicMean[d]; q[n_] := Module[{d = Divisors[n], nd, s, subs, ans = False}, nd = Length[d]; subs = Subsets[d]; Do[s = subs[[k]]; If[Length[s] > 1 && Length[s] <= nd/2 && hQ[s] && hQ[Complement[d, s]], ans = True; Break[]], {k, 1, Length[subs]}]; ans]; Select[Range[300], q]