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 A337605 Number of unordered triples of distinct positive integers summing to n, any two of which have a common divisor > 1. 21
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 4, 0, 4, 1, 5, 0, 9, 0, 8, 3, 10, 0, 17, 1, 14, 5, 16, 1, 25, 1, 21, 8, 26, 2, 37, 1, 30, 15, 33, 2, 49, 2, 44, 16, 44, 2, 64, 6, 54, 21, 56, 3, 87, 5, 65, 30, 70, 9, 101, 5, 80, 34, 98, 6, 121, 6, 96, 52 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,17 LINKS Fausto A. C. Cariboni, Table of n, a(n) for n = 0..10000 EXAMPLE The a(n) triples for n = 12, 16, 18, 22, 27, 55:   (6,4,2)  (8,6,2)   (8,6,4)   (10,8,4)  (12,9,6)  (28,21,6)            (10,4,2)  (9,6,3)   (12,6,4)  (15,9,3)  (30,20,5)                      (10,6,2)  (12,8,2)  (18,6,3)  (35,15,5)                      (12,4,2)  (14,6,2)            (40,10,5)                                (16,4,2)            (25,20,10)                                                    (30,15,10) MATHEMATICA stabQ[u_, Q_]:=Array[#1==#2||!Q[u[[#1]], u[[#2]]]&, {Length[u], Length[u]}, 1, And]; Table[Length[Select[IntegerPartitions[n, {3}], UnsameQ@@#&&stabQ[#, CoprimeQ]&]], {n, 0, 100}] CROSSREFS A014612 intersected with A318719 ranks these partitions. A220377 is the coprime instead of non-coprime version. A318717 counts these partitions of any length, ranked by A318719. A337599 is the non-strict version. A337604 is the ordered non-strict version. A337605*6 is the ordered version. A023023 counts relatively prime 3-part partitions A051424 counts pairwise coprime or singleton partitions. A200976 and A328673 count pairwise non-coprime partitions. A307719 counts pairwise coprime 3-part partitions. A327516 counts pairwise coprime partitions, with strict case A305713. Cf. A000217, A001399, A014612, A082024, A178472, A220377, A284825, A337461, A337561, A337667. Sequence in context: A046769 A145893 A137561 * A082024 A337599 A322337 Adjacent sequences:  A337602 A337603 A337604 * A337606 A337607 A337608 KEYWORD nonn AUTHOR Gus Wiseman, Sep 20 2020 STATUS approved

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Last modified April 20 06:59 EDT 2021. Contains 343125 sequences. (Running on oeis4.)