A319318 - OEIS

A319318

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

1, 1, 1, 1, 2, 1, 3, 2, 3, 3, 5, 2, 6, 5, 5, 5, 8, 5, 9, 6, 8, 9, 11, 6, 11, 11, 11, 10, 14, 9, 16, 12, 14, 15, 15, 11, 19, 17, 17, 14, 22, 15, 22, 18, 18, 21, 25, 16, 24, 21, 23, 22, 28, 21, 26, 22, 26, 27, 32, 20, 35, 30, 27, 27, 31, 27, 38, 30, 33, 29

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OFFSET

1,5

COMMENTS

Note that such partitions are necessarily strict.

LINKS

Table of n, a(n) for n=1..70.

EXAMPLE

The a(31) = 16 partitions are (31), (16,15), (17,14), (18,13), (19,12), (20,11), (21,10), (22,9), (23,8), (24,7), (25,6), (26,5), (27,4), (28,3), (29,2), (15,10,6).

MATHEMATICA

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

CROSSREFS

Cf. A108917, A275972, A289508, A289509, A316313, A319315, A319319, A319320.

Sequence in context: A025797 A035386 A244327 * A029164 A364350 A053262

Adjacent sequences: A319315 A319316 A319317 * A319319 A319320 A319321

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 17 2018

STATUS

approved