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

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, 0, 130, 6, 105, 46, 120, 21, 181, 6, 153, 67, 189, 12, 262, 6, 213, 118, 231, 12, 337, 21, 306, 121, 303, 12, 433, 57, 369, 154, 378, 18, 583, 30, 435, 217, 465

Offset: 0

Author

Gus Wiseman, Sep 20 2020

Keywords

• nonn

Comments

The first relatively prime triple (15,10,6) is counted under a(31).

Examples

			The a(6) = 1 through a(15) = 7 triples (empty columns indicated by dots, A = 10):
  222  .  224  333  226  .  228  .  22A  339
          242       244     246     248  366
          422       262     264     266  393
                    424     282     284  555
                    442     336     2A2  636
                    622     363     428  663
                            426     446  933
                            444     464
                            462     482
                            624     626
                            633     644
                            642     662
                            822     824
                                    842
                                    A22
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..10000

Crossrefs

A014311 intersected with A337666 ranks these compositions.

A337667 counts these compositions of any length.

A335402 lists the positions of zeros.

A337461 is the coprime instead of non-coprime version.

A337599 is the unordered version, with strict case A337605.

A337605*6 is the strict version.

A000741 counts relatively prime 3-part compositions.

A101268 counts pairwise coprime or singleton compositions.

A200976 and A328673 count pairwise non-relatively prime partitions.

A307719 counts pairwise coprime 3-part partitions.

A318717 counts pairwise non-coprime strict partitions.

A333227 ranks pairwise coprime compositions.

Cf. A000217, A001399, A014612, A051424, A082024, A178472, A220377, A284825, A305713, A327516, A333228, A337561.

Programs

Mathematica

stabQ[u_,Q_]:=Array[#1==#2||!Q[u[[#1]],u[[#2]]]&,{Length[u],Length[u]},1,And];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n,{3}],stabQ[#,CoprimeQ]&]],{n,0,100}]