A337563 - OEIS

A337563

Number of pairwise coprime unordered triples of positive integers > 1 summing to n.

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

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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: A308202 A329152 A368581 * A278648 A353508 A029181

Adjacent sequences: A337560 A337561 A337562 * A337564 A337565 A337566

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 21 2020

STATUS

approved