A337664 Number of compositions of n whose set of distinct parts is pairwise coprime, where a singleton is always considered coprime.

1, 1, 2, 4, 8, 16, 30, 58, 111, 210, 396, 750, 1420, 2688, 5079, 9586, 18092, 34157, 64516, 121899, 230373, 435463, 823379, 1557421, 2946938, 5578111, 10561990, 20005129, 37902514, 71832373, 136173273, 258211603, 489738627, 929074448, 1762899110, 3345713034

Offset: 0

Author

Gus Wiseman, Sep 21 2020

Keywords

• nonn

Examples

			The a(0) = 1 through a(5) = 16 compositions:
  ()  (1)  (2)   (3)    (4)     (5)
           (11)  (12)   (13)    (14)
                 (21)   (22)    (23)
                 (111)  (31)    (32)
                        (112)   (41)
                        (121)   (113)
                        (211)   (122)
                        (1111)  (131)
                                (212)
                                (221)
                                (311)
                                (1112)
                                (1121)
                                (1211)
                                (2111)
                                (11111)
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..220

Crossrefs

A304712 is the unordered version.

A337562 is the strict case.

A337602 is the length-3 case.

A337665 does not consider a singleton to be coprime unless it is (1).

A337695 ranks the complement of these compositions.

A000740 counts relatively prime compositions.

A051424 counts pairwise coprime or singleton partitions.

A101268 counts pairwise coprime or singleton compositions.

A305713 counts pairwise coprime strict partitions.

A327516 counts pairwise coprime partitions.

A333227 ranks pairwise coprime compositions.

A333228 ranks compositions whose distinct parts are pairwise coprime.

A337461 counts pairwise coprime length-3 compositions.

A337561 counts pairwise coprime strict compositions.

Cf. A007359, A007360, A087087, A302569, A304709, A307719, A335235, A335238, A335239, A337562, A337603, A337667.

Programs

Mathematica

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],SameQ@@#||CoprimeQ@@Union[#]&]],{n,0,15}]