cp's OEIS Frontend

A337602 Number of ordered triples of positive integers summing to n whose set of distinct parts is pairwise coprime, where a singleton is always considered coprime.

%I A337602 #14 Jan 21 2021 04:23:30
%S A337602 0,0,0,1,3,6,10,9,18,16,24,21,43,24,51,31,54,42,94,45,102,55,99,69,
%T A337602 163,66,150,88,168,96,265,93,228,121,246,126,337,132,315,169,342,162,
%U A337602 487,165,420,217,411,213,619,207,558,259,540,258,784,264,654,325,660
%N A337602 Number of ordered triples of positive integers summing to n whose set of distinct parts is pairwise coprime, where a singleton is always considered coprime.
%H A337602 Fausto A. C. Cariboni, <a href="/A337602/b337602.txt">Table of n, a(n) for n = 0..10000</a>
%e A337602 The a(3) = 1 through a(8) = 18 triples:
%e A337602   (1,1,1)  (1,1,2)  (1,1,3)  (1,1,4)  (1,1,5)  (1,1,6)
%e A337602            (1,2,1)  (1,2,2)  (1,2,3)  (1,3,3)  (1,2,5)
%e A337602            (2,1,1)  (1,3,1)  (1,3,2)  (1,5,1)  (1,3,4)
%e A337602                     (2,1,2)  (1,4,1)  (2,2,3)  (1,4,3)
%e A337602                     (2,2,1)  (2,1,3)  (2,3,2)  (1,5,2)
%e A337602                     (3,1,1)  (2,2,2)  (3,1,3)  (1,6,1)
%e A337602                              (2,3,1)  (3,2,2)  (2,1,5)
%e A337602                              (3,1,2)  (3,3,1)  (2,3,3)
%e A337602                              (3,2,1)  (5,1,1)  (2,5,1)
%e A337602                              (4,1,1)           (3,1,4)
%e A337602                                                (3,2,3)
%e A337602                                                (3,3,2)
%e A337602                                                (3,4,1)
%e A337602                                                (4,1,3)
%e A337602                                                (4,3,1)
%e A337602                                                (5,1,2)
%e A337602                                                (5,2,1)
%e A337602                                                (6,1,1)
%t A337602 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n,{3}],SameQ@@#||CoprimeQ@@Union[#]&]],{n,0,100}]
%Y A337602 The complement in A014311 of A337695 ranks these compositions.
%Y A337602 A220377*6 is the strict case.
%Y A337602 A337600 is the unordered version.
%Y A337602 A337603 does not consider a singleton to be coprime unless it is (1).
%Y A337602 A337664 counts these compositions of any length.
%Y A337602 A000740 counts relatively prime compositions.
%Y A337602 A337561 counts pairwise coprime strict compositions.
%Y A337602 A000217 counts 3-part compositions.
%Y A337602 A001399/A069905/A211540 count 3-part partitions.
%Y A337602 A023023 counts relatively prime 3-part partitions.
%Y A337602 A051424 counts pairwise coprime or singleton partitions.
%Y A337602 A101268 counts pairwise coprime or singleton compositions.
%Y A337602 A305713 counts pairwise coprime strict partitions.
%Y A337602 A327516 counts pairwise coprime partitions.
%Y A337602 A333227 ranks pairwise coprime compositions.
%Y A337602 A333228 ranks compositions whose distinct parts are pairwise coprime.
%Y A337602 A337461 counts pairwise coprime 3-part compositions.
%Y A337602 Cf. A000212, A007359, A087087, A284825, A302696, A304709, A304712, A307719, A328673, A335235, A335238, A337483, A337562, A337601.
%K A337602 nonn
%O A337602 0,5
%A A337602 _Gus Wiseman_, Sep 20 2020