|
|
A337599
|
|
Number of unordered triples of positive integers summing to n, any two of which have a common divisor > 1.
|
|
17
|
|
|
0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 4, 0, 4, 3, 5, 0, 9, 0, 9, 5, 10, 0, 16, 2, 14, 7, 17, 0, 27, 1, 21, 11, 24, 6, 36, 1, 30, 15, 37, 2, 51, 1, 41, 25, 44, 2, 64, 5, 58, 25, 57, 2, 81, 13, 69, 31, 70, 3, 108, 5, 80, 43, 85, 17, 123, 5, 97, 46, 120, 6, 144, 6
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,11
|
|
COMMENTS
|
The first relatively prime triple is (15,10,6), counted under a(31).
|
|
LINKS
|
|
|
EXAMPLE
|
The a(6) = 1 through a(16) = 5 partitions are (empty columns indicated by dots, A..G = 10..16):
222 . 422 333 442 . 444 . 644 555 664 . 666 . 866
622 633 662 663 844 864 884
642 842 933 862 882 A55
822 A22 A42 963 A64
C22 A44 A82
A62 C44
C33 C62
C42 E42
E22 G22
|
|
MATHEMATICA
|
stabQ[u_, Q_]:=Array[#1==#2||!Q[u[[#1]], u[[#2]]]&, {Length[u], Length[u]}, 1, And];
Table[Length[Select[IntegerPartitions[n, {3}], stabQ[#, CoprimeQ]&]], {n, 0, 100}]
|
|
CROSSREFS
|
A284825 is the case that is also relatively prime.
A307719 is the pairwise coprime instead of non-coprime version.
A335402 gives the positions of zeros.
A051424 counts pairwise coprime or singleton partitions.
A101268 counts pairwise coprime or singleton compositions.
A305713 counts strict pairwise coprime partitions.
A327516 counts pairwise coprime partitions.
A333227 ranks pairwise coprime compositions.
A333228 ranks compositions whose distinct parts are pairwise coprime.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|