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

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, 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, 31, 70, 3, 108, 5, 80, 43, 85, 17, 123, 5, 97, 46, 120, 6, 144, 6

Offset: 0

Author

Gus Wiseman, Sep 20 2020

Keywords

• nonn

Comments

First differs from A082024 at a(31) = 1, A082024(31) = 0.

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

Examples

			The a(6) = 1 through a(16) = 5 partitions are (empty columns indicated by dots, A..G = 10..16):
  222  .  422  333  442  .  444  .  644  555  664  .  666  .  866
                    622     633     662  663  844     864     884
                            642     842  933  862     882     A55
                            822     A22       A42     963     A64
                                              C22     A44     A82
                                                      A62     C44
                                                      C33     C62
                                                      C42     E42
                                                      E22     G22
		

Links

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

Crossrefs

A014612 intersected with A337694 ranks these partitions.

A200976 and A328673 count these partitions of any length.

A284825 is the case that is also relatively prime.

A307719 is the pairwise coprime instead of non-coprime version.

A335402 gives the positions of zeros.

A337604 is the ordered version.

A337605 is the strict case.

A051424 counts pairwise coprime or singleton partitions.

A101268 counts pairwise coprime or singleton compositions.

A305713 counts strict pairwise coprime partitions.

A327516 counts pairwise coprime partitions.

A333227 ranks pairwise coprime compositions.

A333228 ranks compositions whose distinct parts are pairwise coprime.

Cf. A000212, A000217, A001840, A018783, A082024, A211540, A220377, A337461.

Programs

Mathematica

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