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A101268
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Number of compositions of n into pairwise relatively prime parts.
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54
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1, 1, 2, 4, 7, 13, 22, 38, 63, 101, 160, 254, 403, 635, 984, 1492, 2225, 3281, 4814, 7044, 10271, 14889, 21416, 30586, 43401, 61205, 85748, 119296, 164835, 226423, 309664, 422302, 574827, 781237, 1060182, 1436368, 1942589, 2622079, 3531152, 4742316, 6348411
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OFFSET
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0,3
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COMMENTS
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Here a singleton is always considered pairwise relatively prime. Compare to A337462. - Gus Wiseman, Oct 18 2020
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LINKS
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FORMULA
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It seems that no formula is known.
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EXAMPLE
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The a(1) = 1 through a(5) = 13 compositions:
(1) (2) (3) (4) (5)
(11) (12) (13) (14)
(21) (31) (23)
(111) (112) (32)
(121) (41)
(211) (113)
(1111) (131)
(311)
(1112)
(1121)
(1211)
(2111)
(11111)
(End)
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MATHEMATICA
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Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], Length[#]<=1||CoprimeQ@@#&]], {n, 0, 10}] (* Gus Wiseman, Oct 18 2020 *)
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CROSSREFS
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A337461 counts these compositions of length 3, with unordered version A307719 and unordered strict version A220377.
A337462 does not consider a singleton to be coprime unless it is (1), with strict version A337561.
A337664 looks only at distinct parts, with non-constant version A337665.
A000740 counts relatively prime compositions, with strict case A332004.
A178472 counts compositions with a common factor.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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