A337600 Number of unordered triples of positive integers summing to n whose set of distinct parts is pairwise coprime, where a singleton is always considered coprime.

0, 0, 0, 1, 1, 2, 3, 3, 4, 5, 5, 6, 9, 7, 10, 8, 11, 11, 18, 12, 19, 13, 19, 17, 30, 16, 28, 20, 31, 23, 47, 23, 42, 26, 45, 27, 60, 31, 57, 35, 61, 37, 85, 38, 75, 43, 74, 47, 108, 45, 98, 52, 96, 56, 136, 54, 115, 64, 117, 67, 175, 65, 139, 76, 144, 75, 195

Offset: 0

Author

Gus Wiseman, Sep 20 2020

Keywords

• nonn

Comments

First differs from A337601 at a(9) = 5, A337601(9) = 4.

Examples

			The a(3) = 1 through a(14) = 10 partitions (A = 10, B = 11, C = 12):
  111  211  221  222  322  332  333  433  443  444  544  554
            311  321  331  431  441  532  533  543  553  743
                 411  511  521  522  541  551  552  661  752
                           611  531  721  722  651  733  761
                                711  811  731  732  751  833
                                          911  741  922  851
                                               831  B11  941
                                               921       A31
                                               A11       B21
                                                         C11
		

Links

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

Crossrefs

A220377 is the strict case.

A304712 counts these partitions of any length.

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

A337601 does not consider a singleton to be coprime unless it is (1).

A337602 is the ordered version.

A337664 counts compositions of this type and any length.

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.

A304709 counts partitions whose distinct parts are pairwise coprime.

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 length-3 compositions.

A337563 counts pairwise coprime length-3 partitions with no 1's.

Cf. A001840, A007359, A007360, A014612, A087087, A284825, A302569, A302696, A328673, A335235, A337603, A337695.

Programs

Mathematica

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

Formula

For n > 0, a(n) = A337601(n) + A079978(n).