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%I #12 Feb 07 2021 00:41:21
%S 1,1,2,4,8,16,30,58,111,210,396,750,1420,2688,5079,9586,18092,34157,
%T 64516,121899,230373,435463,823379,1557421,2946938,5578111,10561990,
%U 20005129,37902514,71832373,136173273,258211603,489738627,929074448,1762899110,3345713034
%N Number of compositions of n whose set of distinct parts is pairwise coprime, where a singleton is always considered coprime.
%H Fausto A. C. Cariboni, <a href="/A337664/b337664.txt">Table of n, a(n) for n = 0..220</a>
%e The a(0) = 1 through a(5) = 16 compositions:
%e () (1) (2) (3) (4) (5)
%e (11) (12) (13) (14)
%e (21) (22) (23)
%e (111) (31) (32)
%e (112) (41)
%e (121) (113)
%e (211) (122)
%e (1111) (131)
%e (212)
%e (221)
%e (311)
%e (1112)
%e (1121)
%e (1211)
%e (2111)
%e (11111)
%t Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],SameQ@@#||CoprimeQ@@Union[#]&]],{n,0,15}]
%Y A304712 is the unordered version.
%Y A337562 is the strict case.
%Y A337602 is the length-3 case.
%Y A337665 does not consider a singleton to be coprime unless it is (1).
%Y A337695 ranks the complement of these compositions.
%Y A000740 counts relatively prime compositions.
%Y A051424 counts pairwise coprime or singleton partitions.
%Y A101268 counts pairwise coprime or singleton compositions.
%Y A305713 counts pairwise coprime strict partitions.
%Y A327516 counts pairwise coprime partitions.
%Y A333227 ranks pairwise coprime compositions.
%Y A333228 ranks compositions whose distinct parts are pairwise coprime.
%Y A337461 counts pairwise coprime length-3 compositions.
%Y A337561 counts pairwise coprime strict compositions.
%Y Cf. A007359, A007360, A087087, A302569, A304709, A307719, A335235, A335238, A335239, A337562, A337603, A337667.
%K nonn
%O 0,3
%A _Gus Wiseman_, Sep 21 2020
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