A316440 Number of integer partitions of n such that every submultiset has an integer average.

1, 1, 2, 2, 4, 2, 6, 2, 7, 5, 8, 2, 13, 2, 10, 10, 14, 2, 20, 2, 17, 15, 14, 2, 32, 3, 16, 22, 25, 2, 40, 2, 27, 30, 20, 4, 58, 2, 22, 40, 40, 2, 64, 2, 40, 53, 26, 2, 93, 3, 30, 64, 54, 2, 94, 4, 58, 78, 32, 2, 138, 2, 34, 96, 75, 10, 131, 2, 76, 111, 48, 2, 192, 2, 40, 138, 99

Offset: 0

Author

Gus Wiseman, Jul 03 2018

Keywords

• nonn

Examples

			The a(12) = 13 partitions:
  (12),
  (6,6), (7,5), (8,4), (9,3), (10,2), (11,1),
  (4,4,4), (6,4,2), (8,2,2),
  (3,3,3,3),
  (2,2,2,2,2,2),
  (1,1,1,1,1,1,1,1,1,1,1,1).
		

Links

• Max Alekseyev, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A067538, A074761, A122768, A143773, A237984, A298423, A316313, A316314.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],And@@IntegerQ/@Mean/@Union[Rest[Subsets[#]]]&]],{n,20}]

Formula

For a prime p, a(p) = 2. - Max Alekseyev, Sep 02 2023

Extensions

a(0) prepended and more terms added by Max Alekseyev, Sep 02 2023