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

1,2

Comments

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

Links

Table of n, a(n) for n=1..14.

Example

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}).

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

Crossrefs

Cf. A027750, A083212, A348713.

Sequence in context: A132398 A073120 A147778 * A209452 A275302 A201596

Adjacent sequences: A348711 A348712 A348713 * A348715 A348716 A348717

Keyword

nonn,more

Author

Amiram Eldar, Oct 31 2021

Status

approved