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

1,1

Links

Table of n, a(n) for n=1..56.

Example

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.

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]

Crossrefs

Cf. A001599, A027750, A083207.

Sequence in context: A074726 A341475 A091013 * A159886 A258914 A241646

Adjacent sequences: A348712 A348713 A348714 * A348716 A348717 A348718

Keyword

nonn

Author

Amiram Eldar, Oct 31 2021

Status

approved