cp's OEIS Frontend

A337664 Number of compositions of n whose set of distinct parts is pairwise coprime, where a singleton is always considered coprime.

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