cp's OEIS Frontend

A337561 Number of pairwise coprime strict compositions of n, where a singleton is not considered coprime unless it is (1).

%I A337561 #13 Jan 19 2021 01:09:01
%S A337561 1,1,0,2,2,4,8,6,16,12,22,40,40,66,48,74,74,154,210,228,242,240,286,
%T A337561 394,806,536,840,654,1146,1618,2036,2550,2212,2006,2662,4578,4170,
%U A337561 7122,4842,6012,6214,11638,13560,16488,14738,15444,16528,25006,41002,32802
%N A337561 Number of pairwise coprime strict compositions of n, where a singleton is not considered coprime unless it is (1).
%H A337561 Fausto A. C. Cariboni, <a href="/A337561/b337561.txt">Table of n, a(n) for n = 0..600</a>
%F A337561 a(n) = A337562(n) - 1 for n > 1.
%e A337561 The a(1) = 1 through a(9) = 12 compositions (empty column shown as dot):
%e A337561    (1)  .  (1,2)  (1,3)  (1,4)  (1,5)    (1,6)  (1,7)    (1,8)
%e A337561            (2,1)  (3,1)  (2,3)  (5,1)    (2,5)  (3,5)    (2,7)
%e A337561                          (3,2)  (1,2,3)  (3,4)  (5,3)    (4,5)
%e A337561                          (4,1)  (1,3,2)  (4,3)  (7,1)    (5,4)
%e A337561                                 (2,1,3)  (5,2)  (1,2,5)  (7,2)
%e A337561                                 (2,3,1)  (6,1)  (1,3,4)  (8,1)
%e A337561                                 (3,1,2)         (1,4,3)  (1,3,5)
%e A337561                                 (3,2,1)         (1,5,2)  (1,5,3)
%e A337561                                                 (2,1,5)  (3,1,5)
%e A337561                                                 (2,5,1)  (3,5,1)
%e A337561                                                 (3,1,4)  (5,1,3)
%e A337561                                                 (3,4,1)  (5,3,1)
%e A337561                                                 (4,1,3)
%e A337561                                                 (4,3,1)
%e A337561                                                 (5,1,2)
%e A337561                                                 (5,2,1)
%t A337561 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],#=={}||UnsameQ@@#&&CoprimeQ@@#&]],{n,0,10}]
%Y A337561 A072706 counts unimodal strict compositions.
%Y A337561 A220377*6 counts these compositions of length 3.
%Y A337561 A305713 is the unordered version.
%Y A337561 A337462 is the not necessarily strict version.
%Y A337561 A000740 counts relatively prime compositions, with strict case A332004.
%Y A337561 A051424 counts pairwise coprime or singleton partitions.
%Y A337561 A101268 considers all singletons to be coprime, with strict case A337562.
%Y A337561 A178472 counts compositions with a common factor > 1.
%Y A337561 A327516 counts pairwise coprime partitions, with strict case A305713.
%Y A337561 A328673 counts pairwise non-coprime partitions.
%Y A337561 A333228 ranks compositions whose distinct parts are pairwise coprime.
%Y A337561 Cf. A007359, A007360, A087087, A216652, A220377, A302569, A307719, A326675, A333227, A337461.
%K A337561 nonn
%O A337561 0,4
%A A337561 _Gus Wiseman_, Sep 18 2020