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%I #11 Nov 02 2021 22:20:29
%S 6,20,24,30,42,48,54,56,60,66,70,72,78,84,88,90,96,102,108,114,120,
%T 126,132,135,138,140,150,156,160,168,174,180,186,190,192,196,198,200,
%U 204,210,216,220,222,224,228,230,234,240,246,252,258,260,264,270,273,276
%N Numbers whose divisors can be partitioned into two disjoint sets with equal arithmetic mean.
%C The arithmetic mean of each of the two subsets is equal to the arithmetic mean of all the divisors of the number.
%C 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.
%H Amiram Eldar, <a href="/A348713/b348713.txt">Table of n, a(n) for n = 1..872</a>
%e 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.
%t 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]
%Y Cf. A027750, A057020, A057021, A083207.
%Y A347063 is a subsequence.
%K nonn
%O 1,1
%A _Amiram Eldar_, Oct 31 2021
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