A337461 Number of pairwise coprime ordered triples of positive integers summing to n.
0, 0, 0, 1, 3, 3, 9, 3, 15, 9, 21, 9, 39, 9, 45, 21, 45, 21, 87, 21, 93, 39, 87, 39, 153, 39, 135, 63, 153, 57, 255, 51, 207, 93, 225, 93, 321, 81, 291, 135, 321, 105, 471, 105, 393, 183, 381, 147, 597, 147, 531, 213, 507, 183, 759, 207, 621, 273, 621, 231
Offset: 0
Keywords
Examples
The a(3) = 1 through a(9) = 9 triples:
(1,1,1) (1,1,2) (1,1,3) (1,1,4) (1,1,5) (1,1,6) (1,1,7)
(1,2,1) (1,3,1) (1,2,3) (1,5,1) (1,2,5) (1,3,5)
(2,1,1) (3,1,1) (1,3,2) (5,1,1) (1,3,4) (1,5,3)
(1,4,1) (1,4,3) (1,7,1)
(2,1,3) (1,5,2) (3,1,5)
(2,3,1) (1,6,1) (3,5,1)
(3,1,2) (2,1,5) (5,1,3)
(3,2,1) (2,5,1) (5,3,1)
(4,1,1) (3,1,4) (7,1,1)
(3,4,1)
(4,1,3)
(4,3,1)
(5,1,2)
(5,2,1)
(6,1,1)
Links
- Fausto A. C. Cariboni, Table of n, a(n) for n = 0..10000
Crossrefs
A000212 counts the unimodal instead of coprime version.
A220377*6 is the strict case.
A307719 is the unordered version.
A337462 counts these compositions of any length.
A337563 counts the case of partitions with no 1's.
A337603 only requires the *distinct* parts to be pairwise coprime.
A337604 is the intersecting instead of coprime version.
A014612 ranks 3-part partitions.
A302696 ranks pairwise coprime partitions.
A327516 counts pairwise coprime partitions.
A333228 ranks compositions whose distinct parts are pairwise coprime.
Programs
-
Mathematica
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n,{3}],CoprimeQ@@#&]],{n,0,30}]