cp's OEIS Frontend

A337599 Number of unordered triples of positive integers summing to n, any two of which have a common divisor > 1.

%I A337599 #12 Jan 13 2021 14:28:44
%S A337599 0,0,0,0,0,0,1,0,1,1,2,0,4,0,4,3,5,0,9,0,9,5,10,0,16,2,14,7,17,0,27,1,
%T A337599 21,11,24,6,36,1,30,15,37,2,51,1,41,25,44,2,64,5,58,25,57,2,81,13,69,
%U A337599 31,70,3,108,5,80,43,85,17,123,5,97,46,120,6,144,6
%N A337599 Number of unordered triples of positive integers summing to n, any two of which have a common divisor > 1.
%C A337599 First differs from A082024 at a(31) = 1, A082024(31) = 0.
%C A337599 The first relatively prime triple is (15,10,6), counted under a(31).
%H A337599 Fausto A. C. Cariboni, <a href="/A337599/b337599.txt">Table of n, a(n) for n = 0..10000</a>
%e A337599 The a(6) = 1 through a(16) = 5 partitions are (empty columns indicated by dots, A..G = 10..16):
%e A337599   222  .  422  333  442  .  444  .  644  555  664  .  666  .  866
%e A337599                     622     633     662  663  844     864     884
%e A337599                             642     842  933  862     882     A55
%e A337599                             822     A22       A42     963     A64
%e A337599                                               C22     A44     A82
%e A337599                                                       A62     C44
%e A337599                                                       C33     C62
%e A337599                                                       C42     E42
%e A337599                                                       E22     G22
%t A337599 stabQ[u_,Q_]:=Array[#1==#2||!Q[u[[#1]],u[[#2]]]&,{Length[u],Length[u]},1,And];
%t A337599 Table[Length[Select[IntegerPartitions[n,{3}],stabQ[#,CoprimeQ]&]],{n,0,100}]
%Y A337599 A014612 intersected with A337694 ranks these partitions.
%Y A337599 A200976 and A328673 count these partitions of any length.
%Y A337599 A284825 is the case that is also relatively prime.
%Y A337599 A307719 is the pairwise coprime instead of non-coprime version.
%Y A337599 A335402 gives the positions of zeros.
%Y A337599 A337604 is the ordered version.
%Y A337599 A337605 is the strict case.
%Y A337599 A051424 counts pairwise coprime or singleton partitions.
%Y A337599 A101268 counts pairwise coprime or singleton compositions.
%Y A337599 A305713 counts strict pairwise coprime partitions.
%Y A337599 A327516 counts pairwise coprime partitions.
%Y A337599 A333227 ranks pairwise coprime compositions.
%Y A337599 A333228 ranks compositions whose distinct parts are pairwise coprime.
%Y A337599 Cf. A000212, A000217, A001840, A018783, A082024, A211540, A220377, A337461.
%K A337599 nonn
%O A337599 0,11
%A A337599 _Gus Wiseman_, Sep 20 2020