A319320 Number of integer partitions of n such that every distinct submultiset has a different LCM.

1, 1, 1, 1, 2, 1, 3, 2, 3, 4, 5, 4, 6, 7, 7, 9, 11, 12, 12, 15, 17, 20, 22, 24, 25, 31, 35, 39, 40, 48, 51, 55, 64, 73, 77, 85, 92, 104, 115, 126, 136, 147, 157, 176, 198, 211, 234, 246, 269, 294, 326, 350, 375, 403, 443, 475, 526, 560, 600, 650

Offset

1,5

Comments

Note that such partitions are necessarily strict.

Links

Table of n, a(n) for n=1..60.

Example

The a(19) = 12 partitions:
  (19),
  (10,9), (11,8), (12,7), (13,6), (14,5), (15,4), (16,3), (17,2),
  (8,6,5), (11,5,3),
  (7,5,4,3).

Mathematica

Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&UnsameQ@@LCM@@@Union[Rest[Subsets[#]]]&]], {n, 30}]

Crossrefs

Cf. A074761, A108917, A275972, A290103, A316313, A316429, A316431, A319315, A319318, A319327.

Sequence in context: A289152 A363708 A285779 * A305194 A303362 A362061

Adjacent sequences: A319317 A319318 A319319 * A319321 A319322 A319323

Keyword

nonn

Author

Gus Wiseman, Sep 17 2018

Status

approved