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A337461 Number of pairwise coprime ordered triples of positive integers summing to n.

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