cp's OEIS Frontend

A337665 Number of compositions of n whose distinct parts are pairwise coprime, where a singleton is not considered coprime unless it is (1).

%I A337665 #10 Feb 07 2021 10:48:59
%S A337665 0,1,1,3,6,15,27,57,108,208,393,749,1415,2687,5076,9583,18088,34156,
%T A337665 64511,121898,230368,435460,823376,1557420,2946931,5578109,10561987,
%U A337665 20005126,37902509,71832372,136173266,258211602,489738622,929074445,1762899107,3345713031
%N A337665 Number of compositions of n whose distinct parts are pairwise coprime, where a singleton is not considered coprime unless it is (1).
%C A337665 A composition of n is a finite sequence of positive integers summing to n.
%H A337665 Fausto A. C. Cariboni, <a href="/A337665/b337665.txt">Table of n, a(n) for n = 0..220</a>
%e A337665 The a(1) = 1 through a(5) = 15 compositions:
%e A337665   (1)  (1,1)  (1,2)    (1,3)      (1,4)
%e A337665               (2,1)    (3,1)      (2,3)
%e A337665               (1,1,1)  (1,1,2)    (3,2)
%e A337665                        (1,2,1)    (4,1)
%e A337665                        (2,1,1)    (1,1,3)
%e A337665                        (1,1,1,1)  (1,2,2)
%e A337665                                   (1,3,1)
%e A337665                                   (2,1,2)
%e A337665                                   (2,2,1)
%e A337665                                   (3,1,1)
%e A337665                                   (1,1,1,2)
%e A337665                                   (1,1,2,1)
%e A337665                                   (1,2,1,1)
%e A337665                                   (2,1,1,1)
%e A337665                                   (1,1,1,1,1)
%t A337665 Table[Length[Join@@Permutations/@Select[IntegerPartitions[n],CoprimeQ@@Union[#]&]],{n,0,15}]
%Y A337665 A000740 is a relatively prime instead of pairwise coprime version.
%Y A337665 A304709 is the unordered version.
%Y A337665 A333228 ranks these compositions.
%Y A337665 A337561 is the strict case.
%Y A337665 A337603 is the length-3 case.
%Y A337665 A337664 considers all singletons to be coprime.
%Y A337665 A051424 counts pairwise coprime or singleton partitions.
%Y A337665 A101268 counts pairwise coprime or singleton compositions.
%Y A337665 A305713 counts pairwise coprime strict partitions.
%Y A337665 A327516 counts pairwise coprime partitions.
%Y A337665 A333227 ranks pairwise coprime compositions.
%Y A337665 A337461 counts pairwise coprime length-3 compositions.
%Y A337665 Cf. A007359, A007360, A302569, A302696, A304712, A335235, A335238, A337562, A337600, A337601, A337602, A337695.
%K A337665 nonn
%O A337665 0,4
%A A337665 _Gus Wiseman_, Sep 22 2020
%E A337665 a(26)-a(35) from _Alois P. Heinz_, Sep 29 2020