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A332004
Number of compositions (ordered partitions) of n into distinct and relatively prime parts.
15
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
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
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.
Sequence in context: A152763 A221666 A086700 * A364669 A104221 A078044
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 04 2020
STATUS
approved