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 A337561 Number of pairwise coprime strict compositions of n, where a singleton is not considered coprime unless it is (1). 32
 1, 1, 0, 2, 2, 4, 8, 6, 16, 12, 22, 40, 40, 66, 48, 74, 74, 154, 210, 228, 242, 240, 286, 394, 806, 536, 840, 654, 1146, 1618, 2036, 2550, 2212, 2006, 2662, 4578, 4170, 7122, 4842, 6012, 6214, 11638, 13560, 16488, 14738, 15444, 16528, 25006, 41002, 32802 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Fausto A. C. Cariboni, Table of n, a(n) for n = 0..600 FORMULA a(n) = A337562(n) - 1 for n > 1. EXAMPLE The a(1) = 1 through a(9) = 12 compositions (empty column shown as dot):    (1)  .  (1,2)  (1,3)  (1,4)  (1,5)    (1,6)  (1,7)    (1,8)            (2,1)  (3,1)  (2,3)  (5,1)    (2,5)  (3,5)    (2,7)                          (3,2)  (1,2,3)  (3,4)  (5,3)    (4,5)                          (4,1)  (1,3,2)  (4,3)  (7,1)    (5,4)                                 (2,1,3)  (5,2)  (1,2,5)  (7,2)                                 (2,3,1)  (6,1)  (1,3,4)  (8,1)                                 (3,1,2)         (1,4,3)  (1,3,5)                                 (3,2,1)         (1,5,2)  (1,5,3)                                                 (2,1,5)  (3,1,5)                                                 (2,5,1)  (3,5,1)                                                 (3,1,4)  (5,1,3)                                                 (3,4,1)  (5,3,1)                                                 (4,1,3)                                                 (4,3,1)                                                 (5,1,2)                                                 (5,2,1) MATHEMATICA Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], #=={}||UnsameQ@@#&&CoprimeQ@@#&]], {n, 0, 10}] CROSSREFS A072706 counts unimodal strict compositions. A220377*6 counts these compositions of length 3. A305713 is the unordered version. A337462 is the not necessarily strict version. A000740 counts relatively prime compositions, with strict case A332004. A051424 counts pairwise coprime or singleton partitions. A101268 considers all singletons to be coprime, with strict case A337562. A178472 counts compositions with a common factor > 1. A327516 counts pairwise coprime partitions, with strict case A305713. A328673 counts pairwise non-coprime partitions. A333228 ranks compositions whose distinct parts are pairwise coprime. Cf. A007359, A007360, A087087, A216652, A220377, A302569, A307719, A326675, A333227, A337461. Sequence in context: A077968 A123958 A048572 * A121173 A160159 A283241 Adjacent sequences:  A337558 A337559 A337560 * A337562 A337563 A337564 KEYWORD nonn AUTHOR Gus Wiseman, Sep 18 2020 STATUS approved

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