OFFSET
1,1
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 31 2021
STATUS
approved