A337601 Number of unordered triples of positive integers summing to n whose set of distinct parts is pairwise coprime, where a singleton is not considered coprime unless it is (1).

0, 0, 0, 1, 1, 2, 2, 3, 4, 4, 5, 6, 8, 7, 10, 7, 11, 11, 17, 12, 19, 12, 19, 17, 29, 16, 28, 19, 31, 23, 46, 23, 42, 25, 45, 27, 59, 31, 57, 34, 61, 37, 84, 38, 75, 42, 74, 47, 107, 45, 98, 51, 96, 56, 135, 54, 115, 63, 117, 67, 174, 65, 139, 75, 144, 75, 194

Offset: 0

Author

Gus Wiseman, Sep 20 2020

Keywords

• nonn

Comments

First differs from A337600 at a(9) = 4, A337600(9) = 5.

Examples

			The a(3) = 1 through a(14) = 10 partitions (A = 10, B = 11, C = 12):
  111  211  221  321  322  332  441  433  443  543  544  554
            311  411  331  431  522  532  533  552  553  743
                      511  521  531  541  551  651  661  752
                           611  711  721  722  732  733  761
                                     811  731  741  751  833
                                          911  831  922  851
                                               921  B11  941
                                               A11       A31
                                                         B21
                                                         C11
		

Links

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

Crossrefs

A014612 intersected with A304711 ranks these partitions.

A220377 is the strict case.

A304709 counts these partitions of any length.

A307719 is the strict case except for any number of 1's.

A337600 considers singletons to be coprime.

A337603 is the ordered version.

A000217 counts 3-part compositions.

A000837 counts relatively prime partitions.

A001399/A069905/A211540 count 3-part partitions.

A023023 counts relatively prime 3-part partitions.

A051424 counts pairwise coprime or singleton partitions.

A101268 counts pairwise coprime or singleton compositions.

A305713 counts pairwise coprime strict partitions.

A327516 counts pairwise coprime partitions.

A333227 ranks pairwise coprime compositions.

A333228 ranks compositions whose distinct parts are pairwise coprime.

A337461 counts pairwise coprime 3-part compositions.

Cf. A001840, A007359, A007360, A087087, A284825, A302696, A304712, A328673, A335238, A337602.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n,{3}],CoprimeQ@@Union[#]&]],{n,0,100}]

Formula

For n > 0, a(n) = A337600(n) - A079978(n).