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A337563 Number of pairwise coprime unordered triples of positive integers > 1 summing to n. 19
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 4, 0, 7, 1, 7, 3, 9, 2, 15, 3, 13, 5, 17, 4, 29, 5, 20, 8, 28, 8, 42, 8, 31, 14, 42, 10, 59, 12, 45, 21, 52, 14, 77, 17, 68, 26, 69, 19, 101, 26, 84, 34, 86, 25, 138, 28, 95, 43, 111, 36, 161, 35, 118, 52, 151 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,13

COMMENTS

Such partitions are necessarily strict.

The Heinz numbers of these partitions are the intersection of A005408 (no 1's), A014612 (triples), and A302696 (coprime).

LINKS

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

EXAMPLE

The a(10) = 1 through a(24) = 15 triples (empty columns indicated by dots, A..J = 10..19):

  532  .  543  .  743  753  754  .  765  B53  875  975  985  B75  987

          732     752       853     873       974  B73  B65  D73  B76

                            952     954       A73  D53  B74       B85

                            B32     972       B54       B83       B94

                                    B43       B72       B92       BA3

                                    B52       D43       D54       C75

                                    D32       D52       D72       D65

                                                        E53       D74

                                                        H32       D83

                                                                  D92

                                                                  F72

                                                                  G53

                                                                  H43

                                                                  H52

                                                                  J32

MATHEMATICA

Table[Length[Select[IntegerPartitions[n, {3}], !MemberQ[#, 1]&&CoprimeQ@@#&]], {n, 0, 30}]

CROSSREFS

A055684 is the version for pairs.

A220377 allows 1's, with non-strict version A307719.

A337485 counts these partitions of any length.

A337563*6 is the ordered version.

A001399(n - 3) = A069905(n) = A211540(n + 2) counts 3-part partitions.

A002865 counts partitions with no 1's, with strict case A025147.

A007359 counts pairwise coprime partitions with no 1's.

A078374 counts relatively prime strict partitions.

A200976 and A328673 count pairwise non-coprime partitions.

A302696 ranks pairwise coprime partitions.

A302698 counts relatively prime partitions with no 1's.

A305713 counts pairwise coprime strict partitions.

A327516 counts pairwise coprime partitions.

A337452 counts relatively prime strict partitions with no 1's.

Cf. A007304, A082024, A101268, A284825, A332004, A337451, A337461, A337462, A337561, A337599, A337601, A337605.

Sequence in context: A053470 A308202 A329152 * A278648 A029181 A261426

Adjacent sequences:  A337560 A337561 A337562 * A337564 A337565 A337566

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 21 2020

STATUS

approved

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Last modified April 11 14:44 EDT 2021. Contains 342886 sequences. (Running on oeis4.)