A337561 Number of pairwise coprime strict compositions of n, where a singleton is not considered coprime unless it is (1).

1, 1, 0, 2, 2, 4, 8, 6, 16, 12, 22, 40, 40, 66, 48, 74, 74, 154, 210, 228, 242, 240, 286, 394, 806, 536, 840, 654, 1146, 1618, 2036, 2550, 2212, 2006, 2662, 4578, 4170, 7122, 4842, 6012, 6214, 11638, 13560, 16488, 14738, 15444, 16528, 25006, 41002, 32802

Offset: 0

Author

Gus Wiseman, Sep 18 2020

Keywords

• nonn

Examples

			The a(1) = 1 through a(9) = 12 compositions (empty column shown as dot):
   (1)  .  (1,2)  (1,3)  (1,4)  (1,5)    (1,6)  (1,7)    (1,8)
           (2,1)  (3,1)  (2,3)  (5,1)    (2,5)  (3,5)    (2,7)
                         (3,2)  (1,2,3)  (3,4)  (5,3)    (4,5)
                         (4,1)  (1,3,2)  (4,3)  (7,1)    (5,4)
                                (2,1,3)  (5,2)  (1,2,5)  (7,2)
                                (2,3,1)  (6,1)  (1,3,4)  (8,1)
                                (3,1,2)         (1,4,3)  (1,3,5)
                                (3,2,1)         (1,5,2)  (1,5,3)
                                                (2,1,5)  (3,1,5)
                                                (2,5,1)  (3,5,1)
                                                (3,1,4)  (5,1,3)
                                                (3,4,1)  (5,3,1)
                                                (4,1,3)
                                                (4,3,1)
                                                (5,1,2)
                                                (5,2,1)
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..600

Crossrefs

A072706 counts unimodal strict compositions.

A220377*6 counts these compositions of length 3.

A305713 is the unordered version.

A337462 is the not necessarily strict version.

A000740 counts relatively prime compositions, with strict case A332004.

A051424 counts pairwise coprime or singleton partitions.

A101268 considers all singletons to be coprime, with strict case A337562.

A178472 counts compositions with a common factor > 1.

A327516 counts pairwise coprime partitions, with strict case A305713.

A328673 counts pairwise non-coprime partitions.

A333228 ranks compositions whose distinct parts are pairwise coprime.

Cf. A007359, A007360, A087087, A216652, A220377, A302569, A307719, A326675, A333227, A337461.

Programs

Mathematica

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],#=={}||UnsameQ@@#&&CoprimeQ@@#&]],{n,0,10}]

Formula

a(n) = A337562(n) - 1 for n > 1.