

A348713


Numbers whose divisors can be partitioned into two disjoint sets with equal arithmetic mean.


2



6, 20, 24, 30, 42, 48, 54, 56, 60, 66, 70, 72, 78, 84, 88, 90, 96, 102, 108, 114, 120, 126, 132, 135, 138, 140, 150, 156, 160, 168, 174, 180, 186, 190, 192, 196, 198, 200, 204, 210, 216, 220, 222, 224, 228, 230, 234, 240, 246, 252, 258, 260, 264, 270, 273, 276
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OFFSET

1,1


COMMENTS

The arithmetic mean of each of the two subsets is equal to the arithmetic mean of all the divisors of the number.
Also, numbers whose divisors can be partitioned into two disjoint sets with equal harmonic mean. This definition is equivalent since the harmonic mean of a subset {d_i} of the divisors of k is equal to k/<k/d_i>, where <k/d_i> is the arithmetic mean over the complementary divisors k/d_i.


LINKS



EXAMPLE

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


MATHEMATICA

q[n_] := Module[{d = Divisors[n], nd, m, s, subs, ans = False}, nd = Length[d]; m = Plus @@ d/nd; subs = Subsets[d]; Do[s = subs[[k]]; If[0 < Length[s] < nd && Mean[s] == m, ans = True; Break[]], {k, 1, Length[subs]}]; ans]; Select[Range[300], q]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



