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A337563 Number of pairwise coprime unordered triples of positive integers > 1 summing to n. 21
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.
Sequence in context: A308202 A329152 A368581 * A278648 A353508 A029181
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 21 2020
STATUS
approved

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Last modified March 28 07:33 EDT 2024. Contains 371235 sequences. (Running on oeis4.)