%I #11 Jan 19 2021 01:09:06
%S 1,1,1,3,3,5,9,7,17,13,23,41,41,67,49,75,75,155,211,229,243,241,287,
%T 395,807,537,841,655,1147,1619,2037,2551,2213,2007,2663,4579,4171,
%U 7123,4843,6013,6215,11639,13561,16489,14739,15445,16529,25007,41003,32803
%N Number of pairwise coprime strict compositions of n, where a singleton is always considered coprime.
%H Fausto A. C. Cariboni, <a href="/A337562/b337562.txt">Table of n, a(n) for n = 0..600</a>
%F a(n > 1) = A337561(n) + 1 for n > 1.
%e The a(1) = 1 through a(9) = 12 compositions:
%e (1) (2) (3) (4) (5) (6) (7) (8) (9)
%e (1,2) (1,3) (1,4) (1,5) (1,6) (1,7) (1,8)
%e (2,1) (3,1) (2,3) (5,1) (2,5) (3,5) (2,7)
%e (3,2) (1,2,3) (3,4) (5,3) (4,5)
%e (4,1) (1,3,2) (4,3) (7,1) (5,4)
%e (2,1,3) (5,2) (1,2,5) (7,2)
%e (2,3,1) (6,1) (1,3,4) (8,1)
%e (3,1,2) (1,4,3) (1,3,5)
%e (3,2,1) (1,5,2) (1,5,3)
%e (2,1,5) (3,1,5)
%e (2,5,1) (3,5,1)
%e (3,1,4) (5,1,3)
%e (3,4,1) (5,3,1)
%e (4,1,3)
%e (4,3,1)
%e (5,1,2)
%e (5,2,1)
%t Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@#&&(Length[#]<=1||CoprimeQ@@#)&]],{n,0,10}]
%Y A007360 is the unordered version, with non-strict version A051424.
%Y A101268 is the not necessarily strict version.
%Y A220377*6 counts these compositions of length 3.
%Y A337561 does not consider a singleton to be coprime unless it is (1), with non-strict version A337462.
%Y A337664 looks only at distinct parts.
%Y A000740 counts relatively prime compositions, with strict case A332004.
%Y A072706 counts unimodal strict compositions.
%Y A178472 counts compositions with a common factor.
%Y A327516 counts pairwise coprime partitions, with strict case A305713.
%Y A328673 counts pairwise non-coprime partitions.
%Y A333228 ranks compositions whose distinct parts are pairwise coprime.
%Y Cf. A087087, A220377, A302569, A307719, A326675, A333227, A335235, A335238, A337461, A337665.
%K nonn
%O 0,4
%A _Gus Wiseman_, Sep 20 2020