A337665 Number of compositions of n whose distinct parts are pairwise coprime, where a singleton is not considered coprime unless it is (1).

0, 1, 1, 3, 6, 15, 27, 57, 108, 208, 393, 749, 1415, 2687, 5076, 9583, 18088, 34156, 64511, 121898, 230368, 435460, 823376, 1557420, 2946931, 5578109, 10561987, 20005126, 37902509, 71832372, 136173266, 258211602, 489738622, 929074445, 1762899107, 3345713031

Offset: 0

Author

Gus Wiseman, Sep 22 2020

Keywords

• nonn

Comments

A composition of n is a finite sequence of positive integers summing to n.

Examples

			The a(1) = 1 through a(5) = 15 compositions:
  (1)  (1,1)  (1,2)    (1,3)      (1,4)
              (2,1)    (3,1)      (2,3)
              (1,1,1)  (1,1,2)    (3,2)
                       (1,2,1)    (4,1)
                       (2,1,1)    (1,1,3)
                       (1,1,1,1)  (1,2,2)
                                  (1,3,1)
                                  (2,1,2)
                                  (2,2,1)
                                  (3,1,1)
                                  (1,1,1,2)
                                  (1,1,2,1)
                                  (1,2,1,1)
                                  (2,1,1,1)
                                  (1,1,1,1,1)
		

Links

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

Crossrefs

A000740 is a relatively prime instead of pairwise coprime version.

A304709 is the unordered version.

A333228 ranks these compositions.

A337561 is the strict case.

A337603 is the length-3 case.

A337664 considers all singletons to be coprime.

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.

A337461 counts pairwise coprime length-3 compositions.

Cf. A007359, A007360, A302569, A302696, A304712, A335235, A335238, A337562, A337600, A337601, A337602, A337695.

Programs

Mathematica

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

Extensions

a(26)-a(35) from Alois P. Heinz, Sep 29 2020