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 A337604 Number of ordered triples of positive integers summing to n, any two of which have a common divisor > 1. 21
 0, 0, 0, 0, 0, 0, 1, 0, 3, 1, 6, 0, 13, 0, 15, 7, 21, 0, 37, 0, 39, 16, 45, 0, 73, 6, 66, 28, 81, 0, 130, 6, 105, 46, 120, 21, 181, 6, 153, 67, 189, 12, 262, 6, 213, 118, 231, 12, 337, 21, 306, 121, 303, 12, 433, 57, 369, 154, 378, 18, 583, 30, 435, 217, 465 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS The first relatively prime triple (15,10,6) is counted under a(31). LINKS Fausto A. C. Cariboni, Table of n, a(n) for n = 0..10000 EXAMPLE The a(6) = 1 through a(15) = 7 triples (empty columns indicated by dots, A = 10):   222  .  224  333  226  .  228  .  22A  339           242       244     246     248  366           422       262     264     266  393                     424     282     284  555                     442     336     2A2  636                     622     363     428  663                             426     446  933                             444     464                             462     482                             624     626                             633     644                             642     662                             822     824                                     842                                     A22 MATHEMATICA stabQ[u_, Q_]:=Array[#1==#2||!Q[u[[#1]], u[[#2]]]&, {Length[u], Length[u]}, 1, And]; Table[Length[Select[Join@@Permutations/@IntegerPartitions[n, {3}], stabQ[#, CoprimeQ]&]], {n, 0, 100}] CROSSREFS A014311 intersected with A337666 ranks these compositions. A337667 counts these compositions of any length. A335402 lists the positions of zeros. A337461 is the coprime instead of non-coprime version. A337599 is the unordered version, with strict case A337605. A337605*6 is the strict version. A000741 counts relatively prime 3-part compositions. A101268 counts pairwise coprime or singleton compositions. A200976 and A328673 count pairwise non-relatively prime partitions. A307719 counts pairwise coprime 3-part partitions. A318717 counts pairwise non-coprime strict partitions. A333227 ranks pairwise coprime compositions. Cf. A000217, A001399, A014612, A051424, A082024, A178472, A220377, A284825, A305713, A327516, A333228, A337561. Sequence in context: A113817 A197151 A083238 * A117782 A317855 A301331 Adjacent sequences:  A337601 A337602 A337603 * A337605 A337606 A337607 KEYWORD nonn AUTHOR Gus Wiseman, Sep 20 2020 STATUS approved

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Last modified April 14 12:11 EDT 2021. Contains 342949 sequences. (Running on oeis4.)