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

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, 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, 3, 87, 5, 65, 30, 70, 9, 101, 5, 80, 34, 98, 6, 121, 6, 96, 52

Offset: 0

Author

Gus Wiseman, Sep 20 2020

Keywords

• nonn

Examples

			The a(n) triples for n = 12, 16, 18, 22, 27, 55:
  (6,4,2)  (8,6,2)   (8,6,4)   (10,8,4)  (12,9,6)  (28,21,6)
           (10,4,2)  (9,6,3)   (12,6,4)  (15,9,3)  (30,20,5)
                     (10,6,2)  (12,8,2)  (18,6,3)  (35,15,5)
                     (12,4,2)  (14,6,2)            (40,10,5)
                               (16,4,2)            (25,20,10)
                                                   (30,15,10)
		

Links

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

Crossrefs

A014612 intersected with A318719 ranks these partitions.

A220377 is the coprime instead of non-coprime version.

A318717 counts these partitions of any length, ranked by A318719.

A337599 is the non-strict version.

A337604 is the ordered non-strict version.

A337605*6 is the ordered version.

A023023 counts relatively prime 3-part partitions

A051424 counts pairwise coprime or singleton partitions.

A200976 and A328673 count pairwise non-coprime partitions.

A307719 counts pairwise coprime 3-part partitions.

A327516 counts pairwise coprime partitions, with strict case A305713.

Cf. A000217, A001399, A014612, A082024, A178472, A220377, A284825, A337461, A337561, A337667.

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}],UnsameQ@@#&&stabQ[#,CoprimeQ]&]],{n,0,100}]