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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 (list; graph; refs; listen; history; text; internal format)
 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 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 * A104221 A078044 A329664 Adjacent sequences:  A332001 A332002 A332003 * A332005 A332006 A332007 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Feb 04 2020 STATUS approved

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Last modified April 10 19:06 EDT 2021. Contains 342853 sequences. (Running on oeis4.)