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%I #15 Jan 19 2021 14:38:22
%S 0,0,0,1,3,3,9,3,15,9,21,9,39,9,45,21,45,21,87,21,93,39,87,39,153,39,
%T 135,63,153,57,255,51,207,93,225,93,321,81,291,135,321,105,471,105,
%U 393,183,381,147,597,147,531,213,507,183,759,207,621,273,621,231
%N Number of pairwise coprime ordered triples of positive integers summing to n.
%H Fausto A. C. Cariboni, <a href="/A337461/b337461.txt">Table of n, a(n) for n = 0..10000</a>
%e The a(3) = 1 through a(9) = 9 triples:
%e (1,1,1) (1,1,2) (1,1,3) (1,1,4) (1,1,5) (1,1,6) (1,1,7)
%e (1,2,1) (1,3,1) (1,2,3) (1,5,1) (1,2,5) (1,3,5)
%e (2,1,1) (3,1,1) (1,3,2) (5,1,1) (1,3,4) (1,5,3)
%e (1,4,1) (1,4,3) (1,7,1)
%e (2,1,3) (1,5,2) (3,1,5)
%e (2,3,1) (1,6,1) (3,5,1)
%e (3,1,2) (2,1,5) (5,1,3)
%e (3,2,1) (2,5,1) (5,3,1)
%e (4,1,1) (3,1,4) (7,1,1)
%e (3,4,1)
%e (4,1,3)
%e (4,3,1)
%e (5,1,2)
%e (5,2,1)
%e (6,1,1)
%t Table[Length[Select[Join@@Permutations/@IntegerPartitions[n,{3}],CoprimeQ@@#&]],{n,0,30}]
%Y A000212 counts the unimodal instead of coprime version.
%Y A220377*6 is the strict case.
%Y A307719 is the unordered version.
%Y A337462 counts these compositions of any length.
%Y A337563 counts the case of partitions with no 1's.
%Y A337603 only requires the *distinct* parts to be pairwise coprime.
%Y A337604 is the intersecting instead of coprime version.
%Y A014612 ranks 3-part partitions.
%Y A302696 ranks pairwise coprime partitions.
%Y A327516 counts pairwise coprime partitions.
%Y A333228 ranks compositions whose distinct parts are pairwise coprime.
%Y Cf. A000217, A001399, A001840, A014311, A101268, A284825, A337562, A326675, A333227, A337601, A337602.
%K nonn
%O 0,5
%A _Gus Wiseman_, Sep 02 2020
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