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 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 (list; graph; refs; listen; history; text; internal format)
 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/, where is the arithmetic mean over the complementary divisors k/d_i. LINKS Amiram Eldar, Table of n, a(n) for n = 1..872 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 Cf. A027750, A057020, A057021, A083207. A347063 is a subsequence. Sequence in context: A243905 A062017 A103678 * A020889 A334817 A084682 Adjacent sequences: A348710 A348711 A348712 * A348714 A348715 A348716 KEYWORD nonn AUTHOR Amiram Eldar, Oct 31 2021 STATUS approved

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Last modified February 25 04:52 EST 2024. Contains 370310 sequences. (Running on oeis4.)