A348714 Numbers whose divisors can be partitioned into two disjoint sets with equal arithmetic mean in a record number of ways.

1, 6, 24, 30, 60, 120, 168, 180, 240, 360, 420, 720, 840, 1260

Offset: 1

Author

Amiram Eldar, Oct 31 2021

Keywords

• nonn
• more

Comments

The corresponding record values are 0, 1, 2, 3, 19, 72, 99, 136, 248, 3094, 10452, 78057, 1323260, 4686578, ...

Examples

			6 is the smallest number whose set of divisors can be partitioned into two disjoint sets with equal arithmetic mean: {3} and {1, 2, 6}.
24 is the smallest number whose set of divisors can be partitioned into two disjoint sets with equal arithmetic mean in two ways: ({3, 12}, {1, 2, 4, 6, 8, 24}) and ({1, 2, 3, 24}, {4, 6, 8, 12}).
		

Crossrefs

Cf. A027750, A083212, A348713.

Programs

Mathematica

c[n_] := Count[Subsets[(d = Divisors[n])], _?(Mean[#] == Mean[Complement[d, #]] &)]/2; cm = -1; s = {}; Do[If[(c1 = c[n]) > cm, cm = c1; AppendTo[s, n]], {n, 1, 250}]; s