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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/<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
A347063 is a subsequence.
Sequence in context: A243905 A062017 A103678 * A020889 A334817 A084682
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.)