A348718 Numbers whose divisors can be partitioned into two disjoint sets without singletons whose arithmetic means are both integers.
6, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96
Offset: 1
Keywords
Examples
6 is a term since its set of divisors, {1, 2, 3, 6}, can be partitioned into the two disjoint sets {1, 3} and {2, 6} whose arithmetic means, 2 and 4 respectively, are both integers.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
amQ[d_] := IntegerQ @ Mean[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 && amQ[s] && amQ[Complement[d, s]], ans = True; Break[]], {k, 1, Length[subs]}]; ans]; Select[Range[100], q]
Comments