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A319320 Number of integer partitions of n such that every distinct submultiset has a different LCM. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A137661 A289152 A285779 * A305194 A303362 A183163

Adjacent sequences:  A319317 A319318 A319319 * A319321 A319322 A319323

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 17 2018

STATUS

approved

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Last modified December 3 11:58 EST 2020. Contains 338900 sequences. (Running on oeis4.)