cp's OEIS Frontend

A337604 Number of ordered triples of positive integers summing to n, any two of which have a common divisor > 1.

%I A337604 #12 Jan 19 2021 21:55:06
%S A337604 0,0,0,0,0,0,1,0,3,1,6,0,13,0,15,7,21,0,37,0,39,16,45,0,73,6,66,28,81,
%T A337604 0,130,6,105,46,120,21,181,6,153,67,189,12,262,6,213,118,231,12,337,
%U A337604 21,306,121,303,12,433,57,369,154,378,18,583,30,435,217,465
%N A337604 Number of ordered triples of positive integers summing to n, any two of which have a common divisor > 1.
%C A337604 The first relatively prime triple (15,10,6) is counted under a(31).
%H A337604 Fausto A. C. Cariboni, <a href="/A337604/b337604.txt">Table of n, a(n) for n = 0..10000</a>
%e A337604 The a(6) = 1 through a(15) = 7 triples (empty columns indicated by dots, A = 10):
%e A337604   222  .  224  333  226  .  228  .  22A  339
%e A337604           242       244     246     248  366
%e A337604           422       262     264     266  393
%e A337604                     424     282     284  555
%e A337604                     442     336     2A2  636
%e A337604                     622     363     428  663
%e A337604                             426     446  933
%e A337604                             444     464
%e A337604                             462     482
%e A337604                             624     626
%e A337604                             633     644
%e A337604                             642     662
%e A337604                             822     824
%e A337604                                     842
%e A337604                                     A22
%t A337604 stabQ[u_,Q_]:=Array[#1==#2||!Q[u[[#1]],u[[#2]]]&,{Length[u],Length[u]},1,And];
%t A337604 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n,{3}],stabQ[#,CoprimeQ]&]],{n,0,100}]
%Y A337604 A014311 intersected with A337666 ranks these compositions.
%Y A337604 A337667 counts these compositions of any length.
%Y A337604 A335402 lists the positions of zeros.
%Y A337604 A337461 is the coprime instead of non-coprime version.
%Y A337604 A337599 is the unordered version, with strict case A337605.
%Y A337604 A337605*6 is the strict version.
%Y A337604 A000741 counts relatively prime 3-part compositions.
%Y A337604 A101268 counts pairwise coprime or singleton compositions.
%Y A337604 A200976 and A328673 count pairwise non-relatively prime partitions.
%Y A337604 A307719 counts pairwise coprime 3-part partitions.
%Y A337604 A318717 counts pairwise non-coprime strict partitions.
%Y A337604 A333227 ranks pairwise coprime compositions.
%Y A337604 Cf. A000217, A001399, A014612, A051424, A082024, A178472, A220377, A284825, A305713, A327516, A333228, A337561.
%K A337604 nonn
%O A337604 0,9
%A A337604 _Gus Wiseman_, Sep 20 2020