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

Offset: 1

Author

Gus Wiseman, Sep 17 2018

Keywords

• nonn

Comments

Note that such partitions are necessarily strict.

Examples

			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).
		

Crossrefs

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

Programs

Mathematica

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