A316313 Number of integer partitions of n such that every distinct submultiset has a different average.

1, 1, 2, 2, 3, 3, 5, 6, 6, 9, 11, 10, 15, 17, 18, 22, 28, 26, 34, 37, 44, 50, 61, 53, 77, 82, 93, 89, 120, 120, 149, 138, 174, 180, 222, 193, 257, 262, 305, 281, 367, 359, 424, 398, 487, 507, 590, 526, 662, 666, 782, 729, 894, 892, 995, 987, 1154, 1188, 1370

Offset: 1

Author

Gus Wiseman, Jun 29 2018

Keywords

• nonn

Comments

Note that such a partition is necessarily strict.

Examples

			The a(8) = 6 integer partitions are (8), (71), (62), (53), (521), (431).
		

Crossrefs

Cf. A000009, A108917, A275972, A276024, A284640, A299702, A301899, A301900, A316271, A316314.

Programs

Mathematica

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