cp's OEIS Frontend

A337605 Number of unordered triples of distinct positive integers summing to n, any two of which have a common divisor > 1.

%I A337605 #11 Jan 13 2021 10:00:20
%S A337605 0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,2,0,4,0,4,1,5,0,9,0,8,3,10,0,17,1,14,
%T A337605 5,16,1,25,1,21,8,26,2,37,1,30,15,33,2,49,2,44,16,44,2,64,6,54,21,56,
%U A337605 3,87,5,65,30,70,9,101,5,80,34,98,6,121,6,96,52
%N A337605 Number of unordered triples of distinct positive integers summing to n, any two of which have a common divisor > 1.
%H A337605 Fausto A. C. Cariboni, <a href="/A337605/b337605.txt">Table of n, a(n) for n = 0..10000</a>
%e A337605 The a(n) triples for n = 12, 16, 18, 22, 27, 55:
%e A337605   (6,4,2)  (8,6,2)   (8,6,4)   (10,8,4)  (12,9,6)  (28,21,6)
%e A337605            (10,4,2)  (9,6,3)   (12,6,4)  (15,9,3)  (30,20,5)
%e A337605                      (10,6,2)  (12,8,2)  (18,6,3)  (35,15,5)
%e A337605                      (12,4,2)  (14,6,2)            (40,10,5)
%e A337605                                (16,4,2)            (25,20,10)
%e A337605                                                    (30,15,10)
%t A337605 stabQ[u_,Q_]:=Array[#1==#2||!Q[u[[#1]],u[[#2]]]&,{Length[u],Length[u]},1,And];
%t A337605 Table[Length[Select[IntegerPartitions[n,{3}],UnsameQ@@#&&stabQ[#,CoprimeQ]&]],{n,0,100}]
%Y A337605 A014612 intersected with A318719 ranks these partitions.
%Y A337605 A220377 is the coprime instead of non-coprime version.
%Y A337605 A318717 counts these partitions of any length, ranked by A318719.
%Y A337605 A337599 is the non-strict version.
%Y A337605 A337604 is the ordered non-strict version.
%Y A337605 A337605*6 is the ordered version.
%Y A337605 A023023 counts relatively prime 3-part partitions
%Y A337605 A051424 counts pairwise coprime or singleton partitions.
%Y A337605 A200976 and A328673 count pairwise non-coprime partitions.
%Y A337605 A307719 counts pairwise coprime 3-part partitions.
%Y A337605 A327516 counts pairwise coprime partitions, with strict case A305713.
%Y A337605 Cf. A000217, A001399, A014612, A082024, A178472, A220377, A284825, A337461, A337561, A337667.
%K A337605 nonn
%O A337605 0,17
%A A337605 _Gus Wiseman_, Sep 20 2020