A337602 Number of ordered 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, 3, 6, 10, 9, 18, 16, 24, 21, 43, 24, 51, 31, 54, 42, 94, 45, 102, 55, 99, 69, 163, 66, 150, 88, 168, 96, 265, 93, 228, 121, 246, 126, 337, 132, 315, 169, 342, 162, 487, 165, 420, 217, 411, 213, 619, 207, 558, 259, 540, 258, 784, 264, 654, 325, 660

Offset

0,5

Links

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

Example

The a(3) = 1 through a(8) = 18 triples:
  (1,1,1)  (1,1,2)  (1,1,3)  (1,1,4)  (1,1,5)  (1,1,6)
           (1,2,1)  (1,2,2)  (1,2,3)  (1,3,3)  (1,2,5)
           (2,1,1)  (1,3,1)  (1,3,2)  (1,5,1)  (1,3,4)
                    (2,1,2)  (1,4,1)  (2,2,3)  (1,4,3)
                    (2,2,1)  (2,1,3)  (2,3,2)  (1,5,2)
                    (3,1,1)  (2,2,2)  (3,1,3)  (1,6,1)
                             (2,3,1)  (3,2,2)  (2,1,5)
                             (3,1,2)  (3,3,1)  (2,3,3)
                             (3,2,1)  (5,1,1)  (2,5,1)
                             (4,1,1)           (3,1,4)
                                               (3,2,3)
                                               (3,3,2)
                                               (3,4,1)
                                               (4,1,3)
                                               (4,3,1)
                                               (5,1,2)
                                               (5,2,1)
                                               (6,1,1)

Mathematica

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

Crossrefs

The complement in A014311 of A337695 ranks these compositions.

A220377*6 is the strict case.

A337600 is the unordered version.

A337603 does not consider a singleton to be coprime unless it is (1).

A337664 counts these compositions of any length.

A000740 counts relatively prime compositions.

A337561 counts pairwise coprime strict compositions.

A000217 counts 3-part compositions.

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. A000212, A007359, A087087, A284825, A302696, A304709, A304712, A307719, A328673, A335235, A335238, A337483, A337562, A337601.

Sequence in context: A009019 A198467 A198456 * A360946 A032570 A130483

Adjacent sequences: A337599 A337600 A337601 * A337603 A337604 A337605

Keyword

nonn

Author

Gus Wiseman, Sep 20 2020

Status

approved