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

0,3

Links

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

Example

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)

Mathematica

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

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.

Sequence in context: A238869 A326333 A036011 * A104501 A328546 A242697

Adjacent sequences: A325853 A325854 A325855 * A325857 A325858 A325859

Keyword

nonn

Author

Gus Wiseman, May 31 2019

Status

approved