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A337605
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Number of unordered triples of distinct positive integers summing to n, any two of which have a common divisor > 1.
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22
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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
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OFFSET
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0,17
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LINKS
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EXAMPLE
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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)
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MATHEMATICA
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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}]
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CROSSREFS
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A220377 is the coprime instead of non-coprime version.
A337604 is the ordered non-strict version.
A023023 counts relatively prime 3-part partitions
A051424 counts pairwise coprime or singleton partitions.
A307719 counts pairwise coprime 3-part partitions.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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