A332004 Number of compositions (ordered partitions) of n into distinct and relatively prime parts.

1, 1, 0, 2, 2, 4, 8, 12, 16, 24, 52, 64, 88, 132, 180, 344, 416, 616, 816, 1176, 1496, 2736, 3232, 4756, 6176, 8756, 11172, 15576, 24120, 30460, 41456, 55740, 74440, 97976, 130192, 168408, 256464, 315972, 429888, 558192, 749920, 958264, 1274928, 1621272, 2120288, 3020256

Offset

0,4

Comments

Moebius transform of A032020.

Ranking these compositions using standard compositions (A066099) gives the intersection of A233564 (strict) with A291166 (relatively prime). - Gus Wiseman, Oct 18 2020

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Index entries for sequences related to compositions

Example

a(6) = 8 because we have [5, 1], [3, 2, 1], [3, 1, 2], [2, 3, 1], [2, 1, 3], [1, 5], [1, 3, 2] and [1, 2, 3].
From Gus Wiseman, Oct 18 2020: (Start)
The a(1) = 1 through a(8) = 16 compositions (empty column indicated by dot):
  (1)  .  (1,2)  (1,3)  (1,4)  (1,5)    (1,6)    (1,7)
          (2,1)  (3,1)  (2,3)  (5,1)    (2,5)    (3,5)
                        (3,2)  (1,2,3)  (3,4)    (5,3)
                        (4,1)  (1,3,2)  (4,3)    (7,1)
                               (2,1,3)  (5,2)    (1,2,5)
                               (2,3,1)  (6,1)    (1,3,4)
                               (3,1,2)  (1,2,4)  (1,4,3)
                               (3,2,1)  (1,4,2)  (1,5,2)
                                        (2,1,4)  (2,1,5)
                                        (2,4,1)  (2,5,1)
                                        (4,1,2)  (3,1,4)
                                        (4,2,1)  (3,4,1)
                                                 (4,1,3)
                                                 (4,3,1)
                                                 (5,1,2)
                                                 (5,2,1)
(End)

Mathematica

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@#&&GCD@@#<=1&]], {n, 0, 15}] (* Gus Wiseman, Oct 18 2020 *)

Crossrefs

Cf. A007360, A032020, A108700, A302698.

A000740 is the non-strict version.

A078374 is the unordered version (non-strict: A000837).

A101271*6 counts these compositions of length 3 (non-strict: A000741).

A337561/A337562 is the pairwise coprime instead of relatively prime version (non-strict: A337462/A101268).

A289509 gives the Heinz numbers of relatively prime partitions.

A333227/A335235 ranks pairwise coprime compositions.

Cf. A001523, A178472, A216652, A289508, A291166, A333228.

Sequence in context: A152763 A221666 A086700 * A364669 A104221 A078044

Adjacent sequences: A332001 A332002 A332003 * A332005 A332006 A332007

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 04 2020

Status

approved