A325856 Number of integer partitions of n such that every pair of distinct parts has a different product.

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 76, 100, 133, 171, 225, 287, 369, 467, 592, 740, 931, 1155, 1435, 1767, 2178, 2661, 3254, 3953, 4798, 5793, 6991, 8390, 10069, 12022, 14346, 17054, 20255, 23960, 28334, 33390, 39308, 46148, 54116, 63295, 73967, 86224

Offset: 0

Author

Gus Wiseman, May 31 2019

Keywords

• nonn

Examples

			The five partitions of 15 not satisfying the condition are:
  (8,4,2,1)
  (6,4,3,2)
  (6,3,3,2,1)
  (6,3,2,2,1,1)
  (6,3,2,1,1,1,1)
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..150

Crossrefs

The subset case is A196724.

The maximal case is A325859.

The integer partition case is A325856.

The strict integer partition case is A325855.

Cf. A002033, A108917, A143823, A325853, A325854, A325857, A325858, A325877.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],UnsameQ@@Times@@@Subsets[Union[#],{2}]&]],{n,0,30}]