A337664 - OEIS

A337664

Number of compositions of n whose set of distinct parts is pairwise coprime, where a singleton is always considered coprime.

%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