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

0,4

Comments

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

Links

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

Example

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)

Mathematica

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

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.

Sequence in context: A280839 A134774 A264686 * A165729 A348378 A000740

Adjacent sequences: A337662 A337663 A337664 * A337666 A337667 A337668

Keyword

nonn

Author

Gus Wiseman, Sep 22 2020

Extensions

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

Status

approved