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 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 First differs from A082024 at a(31) = 1, A082024(31) = 0. The first relatively prime triple is (15,10,6), 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(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 A014612 intersected with A337694 ranks these partitions. A200976 and A328673 count these partitions of any length. 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. A337604 is the ordered version. A337605 is the strict case. 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. Cf. A000212, A000217, A001840, A018783, A082024, A211540, A220377, A337461. Sequence in context: A137561 A337605 A082024 * A322337 A211008 A286663 Adjacent sequences:  A337596 A337597 A337598 * A337600 A337601 A337602 KEYWORD nonn AUTHOR Gus Wiseman, Sep 20 2020 STATUS approved

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Last modified April 10 08:09 EDT 2021. Contains 342845 sequences. (Running on oeis4.)