cp's OEIS Frontend

A337603 Number of ordered triples of positive integers summing to n whose set of distinct parts is pairwise coprime, where a singleton is not considered coprime unless it is (1).

%I A337603 #12 Jan 21 2021 04:23:39
%S A337603 0,0,0,1,3,6,9,9,18,15,24,21,42,24,51,30,54,42,93,45,102,54,99,69,162,
%T A337603 66,150,87,168,96,264,93,228,120,246,126,336,132,315,168,342,162,486,
%U A337603 165,420,216,411,213,618,207,558,258,540,258,783,264,654,324,660
%N A337603 Number of ordered triples of positive integers summing to n whose set of distinct parts is pairwise coprime, where a singleton is not considered coprime unless it is (1).
%H A337603 Fausto A. C. Cariboni, <a href="/A337603/b337603.txt">Table of n, a(n) for n = 0..10000</a>
%e A337603 The a(3) = 1 through a(8) = 18 triples:
%e A337603   (1,1,1)  (1,1,2)  (1,1,3)  (1,1,4)  (1,1,5)  (1,1,6)
%e A337603            (1,2,1)  (1,2,2)  (1,2,3)  (1,3,3)  (1,2,5)
%e A337603            (2,1,1)  (1,3,1)  (1,3,2)  (1,5,1)  (1,3,4)
%e A337603                     (2,1,2)  (1,4,1)  (2,2,3)  (1,4,3)
%e A337603                     (2,2,1)  (2,1,3)  (2,3,2)  (1,5,2)
%e A337603                     (3,1,1)  (2,3,1)  (3,1,3)  (1,6,1)
%e A337603                              (3,1,2)  (3,2,2)  (2,1,5)
%e A337603                              (3,2,1)  (3,3,1)  (2,3,3)
%e A337603                              (4,1,1)  (5,1,1)  (2,5,1)
%e A337603                                                (3,1,4)
%e A337603                                                (3,2,3)
%e A337603                                                (3,3,2)
%e A337603                                                (3,4,1)
%e A337603                                                (4,1,3)
%e A337603                                                (4,3,1)
%e A337603                                                (5,1,2)
%e A337603                                                (5,2,1)
%e A337603                                                (6,1,1)
%t A337603 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n,{3}],CoprimeQ@@Union[#]&]],{n,0,100}]
%Y A337603 A014311 intersected with A333228 ranks these compositions.
%Y A337603 A220377*6 is the strict case.
%Y A337603 A337461 is the strict case except for any number of 1's.
%Y A337603 A337601 is the unordered version.
%Y A337603 A337602 considers all singletons to be coprime.
%Y A337603 A337665 counts these compositions of any length, ranked by A333228 with complement A335238.
%Y A337603 A000217(n - 2) counts 3-part compositions.
%Y A337603 A001399(n - 3) = A069905(n) = A211540(n + 2) counts 3-part partitions.
%Y A337603 A007318 and A097805 count compositions by length.
%Y A337603 A051424 counts pairwise coprime or singleton partitions.
%Y A337603 A101268 counts pairwise coprime or singleton compositions.
%Y A337603 A304711 ranks partitions whose distinct parts are pairwise coprime.
%Y A337603 A305713 counts strict pairwise coprime partitions.
%Y A337603 A327516 counts pairwise coprime partitions, with strict case A305713.
%Y A337603 A333227 ranks pairwise coprime compositions.
%Y A337603 Cf. A000740, A001840, A007359, A087087, A178472, A284825, A302696, A307719, A335235, A337561, A337695.
%K A337603 nonn
%O A337603 0,5
%A A337603 _Gus Wiseman_, Sep 20 2020